Turbine blade airfoil

ABSTRACT

An airfoil comprises an external surface formed in substantial conformance with a plurality of cross sections. Each of the cross sections has an axial chord and an offset at a corresponding fractional span as set forth in Table 2. Each of the cross sections is described by a set of Cartesian coordinates defined at the corresponding fractional span as set forth in Table 4.

CROSS-REFERENCE TO RELATED APPLICATION

This application is related to co-pending application TURBINE VANEAIRFOIL by Jason L. O'Hearn et al., application Ser. No. 12/877,703,filed on even date herewith.

BACKGROUND

The present invention relates generally to rotary engines, andspecifically to rotor and stator airfoils for gas turbine engines andother turbomachinery. In particular, the invention relates to airfoilgeometry for blades and vanes subject to high velocity working fluidflow, including transonic flow applications.

Gas turbine engines include a variety of rotary-type internal combustionengines and combustion turbines, with applications in industrial powergeneration, aviation and transportation. The core of the gas turbineengine typically comprises a compressor, a combustor and a turbine,which are arranged in flow series with an upstream inlet and downstreamexhaust. Incoming air is compressed in the compressor and mixed withfuel in the combustor, then ignited to generate hot combustion gas. Theturbine generates rotational energy from the hot combustion gas, andcooler, expanded combustion products are exhausted downstream.

The compressor and turbine sections are usually arranged into one ormore differentially rotating spools. The spools are further divided intostages, or alternating rows of blades and vanes. The blades and vanesgenerally have airfoil-shaped cross sections, which are designed toaccelerate, turn and compress the working fluid flow, and to generatelift that is converted to rotational energy in the turbine.

In industrial gas turbines, power is delivered via an output shaftcoupled to an electrical generator or other load, typically utilizing anexternal gearbox. Other configurations include turbofan, turboprop,turbojet and turboshaft engines for fixed-wing aircraft and helicopters,and specialized turbine engines for marine and land-basedtransportation, including naval vessels, trains and armored vehicles.

In turboprop and turboshaft engines the turbine drives a propeller orrotor, typically using a reduction gearbox to control blade speed.Turbojets generate thrust primarily from the exhaust, while turbofansdrive a fan to accelerate flow around the engine core. Commercialturbofans are typically ducted, but unducted designs are also known.Some turbofans also utilize a geared drive to provide greater fan speedcontrol, for example to reduce noise and increase engine efficiency, orto increase or decrease specific thrust.

Aviation turbines generally utilize two and three-spool configurations,with a corresponding number of coaxially rotating turbine and compressorsections. In two-spool designs the high pressure turbine drives a highpressure compressor, forming the high pressure spool or high spool. Thelow spool drives the fan, or a shaft for the rotor or propeller, and mayinclude one or more low pressure compressor stages. Aviation turbinesalso power auxiliary devices including electrical generators, hydraulicpumps and elements of the environmental control system, for exampleusing bleed air from the compressor or via an accessory gearbox.

In high-bypass turbofans, most of the thrust is generated by the fan.Variable-area nozzle surfaces can be deployed to regulate the bypasspressure and improve fan performance, particularly during takeoff andlanding. Low-bypass turbofans provide greater specific thrust but arelouder and less fuel efficient, and are more common on military jets andother high-performance aircraft. High-bypass turbofans utilizevariable-area nozzle systems to regulate exhaust speed and specificthrust. Afterburner assemblies are typically used on military jets forshort-term thrust augmentation.

In general, gas turbine engine performance is constrained by the needfor higher compression ratios and combustion temperatures, whichincrease efficiency and output, versus the cost of increased wear andtear on engine components, including blade and vane airfoils. Thesetradeoffs are particularly relevant in the turbine stages downstream ofthe combustor, where gas path temperatures are elevated, and in otherturbine and compressor sections subject to high velocity, high pressureworking fluid flow, including transonic flow along at least part of theairfoil surface.

Unfortunately, these environments require complex non-linear analysisand modeling techniques, making practical results difficult toaccurately predict. High temperature, high pressure and transonic fluidflows also present a combination of engineering and design challenges,emphasizing the need for stress-resistant airfoil geometries that reduceshock-related losses and increase lift and turning efficiency, whileimproving engine performance and reducing long-term maintenance costs.

SUMMARY

This invention concerns an airfoil for a turbine. The airfoil has anexternal surface formed in substantial conformance with a plurality ofcross sections, and each of the cross sections has an axial chord and anoffset at a corresponding fractional span. The axial chords, offsets andfractional spans are provided in Table 1.

Each of the cross sections is described by a set of Cartesiancoordinates defined at the corresponding fractional span, as provided inTable 3. For each cross section, the Cartesian coordinates, chordlength, fractional span and offset are scalable based on the root chordlength, span height, and root pitch of the airfoil.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a cross-sectional view of a gas turbine engine.

FIG. 2 is a side view of a turbine assembly for the gas turbine engine.

FIG. 3A is an axial view of a vane ring for a turbine.

FIG. 3B is an axial view of a rotor stage for a turbine.

FIG. 4A is a perspective view of a stator vane for the vane ring.

FIG. 4B is a perspective view of a rotor blade for the rotor stage.

FIG. 5 is a schematic view of a turbine stage, showing the gas flowpath.

FIG. 6A is a stacking section view of a vane airfoil.

FIG. 6B is a stacking section view of a blade airfoil.

FIG. 7 is cross sectional view of representative airfoil sections.

DETAILED DESCRIPTION

FIG. 1 is a cross-sectional view of gas turbine engine 10. In thisparticular embodiment, gas turbine engine 10 comprises a turbofan enginewith fan 12 positioned upstream of bypass duct 14. Bypass duct 14 isoriented about a turbine core comprising compressor section 16,combustor 18 and turbine section 20, which are arranged in flow serieswith upstream inlet 22 and downstream outlet 24.

Turbine section 20 comprises high pressure (HP) turbine 30 and lowpressure (LP) turbine 31. Compressor section 16 comprises high pressurecompressor 32 and low pressure compressor 33. High pressure turbine 30is coupled to high pressure compressor 32 via HP shaft 34, forming thehigh pressure spool or high spool. Low pressure turbine 31 is coupled tolow pressure compressor 33 and fan 12 via LP shaft 36, forming the lowpressure spool or low spool. Shafts 34 and 36 are mounted coaxiallyabout turbine axis (centerline) C_(L), and rotate at different speeds.

Compressor and turbine sections 16 and 20 are subdivided into a numberof stages formed by alternating rows of vane and blade airfoils. Asshown in FIG. 1, for example, high pressure turbine 30 includes a firststage vane ring with a plurality of stationary vanes 26 and a firststage rotor with a plurality of rotating blades 28, each having airfoilgeometries selected for high lift, low loss turbine operation, withimproved efficiency and increased engine performance. Alternatively,vanes 26 and blades 28 are deployed either individually or incombination, and are located in any of the turbine stages, or in acompressor stage.

Fan 12 comprises a number of fan blades arranged around a disk or otherrotating member. Fan 12 is coupled to LP turbine 31 via LP shaft 36,which drives fan 12 to provide thrust by accelerating flow throughbypass duct 14. Depending on embodiment, fan 12 can be configured forhigh-bypass operation in a commercial or regional jet, or for low-bypassoperation in a high-performance aircraft such as a military jet fighter.Fan 12 may also be coupled to geared fan drive mechanism 38, providingadditional fan speed control.

In operation of gas turbine engine 10, incoming airflow F₁ enters inlet22 and divides into bypass and core flows F_(B) and F_(C), downstream offan 12. Bypass flow F_(B) propagates through bypass duct 14, and coreflow F_(c) is directed into compressor section 16.

High and low pressure compressors 32 and 33 compress core flow F_(c) forcombustor 18. Compressed air is mixed with fuel in combustor 18, andignited to produce hot combustion gas. The combustion gas exitscombustor 18 and enters high pressure turbine 30, encountering turbinevanes 26 and blades 28.

Vanes 26 turn and accelerate the flow, and blades 28 generate lift torotate HP shaft 34 and drive high pressure compressor 32. Partiallyexpanded combustion gas enters low pressure turbine 31, driving lowpressure compressor 33 and fan 12 via LP shaft 36. Spent combustion gasexits turbine engine 10 at outlet or exhaust nozzle 24.

Depending on configuration, low pressure compressor 32 may also beomitted, or may function as an intermediate pressure (IP) compressor.Alternatively, gas turbine engine 10 utilizes a three-spool design withseparate low, intermediate and high pressure spools. In furtherembodiments, gas turbine engine 10 comprises an unducted turbofan,turboprop or turboshaft engine, or an industrial gas turbine, and thespool configuration varies accordingly.

The thermodynamic efficiency of any turbine engine depends on thepressure ratio, defined as the ratio of the pressure measured at inlet22 and aft of high pressure compressor 32. In general, higher overallpressure ratios offer increased efficiency and improved engineperformance, including greater specific thrust. High overall pressureratios also raise the peak gas path temperature, core pressure and flowrate, increasing thermal and mechanical stress on engine componentsincluding vanes 26 and blades 28.

Overall engine performance thus depends upon the ability of turbinevanes 26 and blades 28 to operate efficiently when subject to thermaland mechanical stresses. High efficiency, low loss and stress resistantairfoil designs also reduce operating and maintenance requirements,improving engine reliability and increasing service life.

FIG. 2 is a side view of turbine assembly 39 with stator vane 26 androtor blade 28. In this particular embodiment vane 26 and blade 28 arelocated downstream of the combustor, for example in the first stage of ahigh pressure turbine assembly as shown in FIG. 1.

Turbine assembly 39 forms an annular flowpath for combustion gas,bounded at inner diameter (ID) ring 40 and outer diameter (OD) ring 42.Vane 26 extends radially along airfoil 44, from inner platform 46 atinner ring 40 to outer platform or shroud 48 at outer ring 42. Blade 28extends radially along airfoil 50, from platform 52 at the inner flowmargin to airfoil tip 54 at the outer flow margin, opposite platform 52and facing turbine casing 56.

Vane 26 is attached to a static turbine component such as casing 56 orturbine support 58, or both. Vane 26 turns and accelerates the workingfluid as it flows through turbine assembly 39. Based on the particulargeometry of airfoil 44, turbine vane 26 also guides flow along thesurfaces of platform 46 and shroud 48.

Rotor blade 28 is mounted to a rotating component such as turbine disk60, for example using a fir tree, dovetail or other blade attachment 62capable of retaining blade 28 when subject to centripetal forces at highrotational speed. Turbine blade 28 generates lift based on the geometryof airfoil 56, and shapes flow along the inner flowpath at platform 52.

Blade 28 operates with rotational clearance between airfoil 50 at tip 54and the outer flow boundary at turbine casing 56. Depending onembodiment, airfoil tip 54 may accommodate an abradable seal arrangementor other seal structure to reduce losses. Additional sealing structuresare typically provided between turbine support 58 and rotor disk 60, andat other locations in the turbine assembly.

FIG. 3A is a schematic view of turbine vane ring 64, taken in adownstream axial direction along turbine axis C_(L) of FIG. 1. Turbinevane ring 64 comprises a plurality of vanes 26, which are arrangedcircumferentially about axis C_(L) to form inner ring 40 at platform 46,with outer ring 42 at shroud 48. In one particular embodiment, vane ring64 consists of forty-four turbine vanes 26, but the number variesaccording to engine size and configuration.

Turbine vanes 26 extend from ID ring 40 at platform 46 to OD ring 42 atshroud 48. Inner turbine ring 40 is oriented about the engine axis atradial distance R_(root) from axis C_(L) to the root section of vanes26. Outer turbine ring 42 located at radial distance R_(root) plus thespan height, where the span height is measured from the root section tothe tip section.

In one embodiment, individual turbine vanes 26 are attached to staticturbine support structures to form inner and outer flow rings 40 and 42at platform 46 and shroud 48, respectively. Alternatively, a number ofvanes 26 are assembled or manufactured together, for example in vanepairs, triplets or other groupings. In further embodiments, vane ring 64is formed in axially split vane ring sections, or as a complete annularstructure that is attached to the rest of the turbine assembly as aunit.

When exposed to high gas path temperatures, turbine vanes 26 areconfigured for interior impingement cooling, exterior film cooling, or acombination thereof. In these embodiments, cooling fluid is supplied viacouplings to internal cooling passages in platform 46, shroud 48, orboth.

FIG. 3B is a schematic view of turbine rotor stage 66, taken in adownstream axial direction along turbine axis C_(L). Turbine rotor stage66 comprises a plurality of blades 28, which are arrangedcircumferentially about axis C_(L) with platforms 52 forming the IDflowpath. In one particular embodiment, rotor stage 66 consists offorty-four turbine blades 28, but the number varies according to enginesize and configuration.

Turbine blades 28 extend radially from platform 52 to airfoil tip 54.Root radius R_(root) is measured from axis C_(L) to the root section ofairfoil 50, but the vane and blade platforms do not necessarily alignand root radius R_(root) typically varies between the vane ring androtor stages.

In one embodiment, turbine blades 28 are individually attached to arotor disk, hub, shaft or other rotational component with platforms 46forming the inner flow boundary. Alternatively, blades 28 are attachedin pairs or other blade groupings, or formed as a unit with the rotordisk or hub. In cooled embodiments, the blade attachments accommodatefluid couplings to internal flow passages for impingement or filmcooling, or a combination thereof.

FIG. 4A is a perspective view of turbine vane 26 with airfoil 44.Airfoil 44 extends radially from platform 46 to shroud 48, and axiallyfrom leading edge 68 to trailing edge 70. In this particular embodiment,shroud 48 is attached to airfoil 44 at the tip section, and coupled to astatic turbine structure. Alternatively, turbine vane 26 is unshrouded,and mounted in cantilever fashion with airfoil portion 44 orientedeither inward or outward. In these embodiments, the tip section ofairfoil 44 is generally positioned in rotational clearance with respectto a disk, drum, hub or other rotating flow boundary.

FIG. 4B is a perspective view of turbine rotor blade 28 with airfoil 50.Airfoil 50 extends radially from platform 52 to tip 54, and axially fromleading edge 72 to trailing edge 74. In this particular embodiment,airfoil 50 is unshrouded, with tip 54 positioned in rotational clearancewith respect to a turbine casing or other flow boundary. Alternatively,an outer platform or shroud is coupled to airfoil 50 at tip 54.

Turbine vanes 26 and blades 28 are formed of a high strength, heatresistant material such as a nickel-based or cobalt-based superalloy, orof a high temperature, stress resistant ceramic or composite material.One or more thermal barrier coatings, abrasion-resistant coatings orother protective coatings are typically applied to selected surfaces,for example the leading or trailing edge, the tip or root section of theairfoil, or the platform or shroud. In cooled embodiments, internalfluid passages and external cooling apertures provide for a combinationof impingement and film cooling.

Airfoil, blade and vane geometries are described in terms of Cartesiancoordinates defined along x, y and z axes. As shown in FIGS. 4A and 4B,the x axis is defined in a substantially downstream axial direction, they axis is defined in a substantially circumferential or rotationaldirection, and the z axis is defined in a substantially radialdirection. The coordinates are discussed below with respect to theparticular blade, vane and airfoil configurations FIGS. 6A, 6B and 7.

FIG. 5 is a schematic view of turbine stage 80, illustrating flowgeometry. Stator vanes 26 and rotor blades 28 are shown with airfoils 44and 50 in cross section, taken along line A-A of FIG. 4A and line B-B ofFIG. 4B, respectively.

Turbine stage 80 is a first, second or higher-order stage of a turbineapparatus, for example in a high, low or intermediate pressure turbineor compressor spool. Turbine stage 80 utilizes either of airfoils 44 andairfoils 50 independently, or both airfoils 44 and airfoils 50 together.

Turbine vanes 26 comprise airfoils 44 with concave high pressuresurfaces 82 (top side in FIG. 5) and convex low pressure (suction)surfaces 84 (bottom). High and low pressure surfaces 82 and 84 extenddownstream from leading edge 68 to trailing edge 70, defining turbinevane airfoils 44 therebetween.

Turbine blades 28 comprise airfoils 50 with high pressure surfaces 86(bottom side in FIG. 5) and low pressure (suction) surfaces 88 (top).High and low pressure surfaces 86 and 88 extend from leading edge 72 totrailing edge 74, defining turbine blade airfoils 50 therebetween. PitchP is determined between adjacent blade or vane airfoils at a particularradial height or fractional span, for example at vane leading edge 68 orblade leading edge 72.

Turbine vanes 26 and blades 28 are shown in a stacked or “unwrapped”view to illustrate the flow of working fluid. Vane and blade airfoils 44and 50 each provide for low loss, high lift turbine operation withefficient turning and acceleration of the working fluid flow, includingregions of transonic flow along the airfoil surfaces.

In turbine operation, flow F is incident in a substantially axialdirection onto leading edge 68 of vanes 26, with blades 28 rotating pasttrailing edge 70. Vane airfoils 44 turn and accelerate the working fluidalong pressure and suction surfaces 82 and 84, generating flow F′ ontoleading edge 72 of blades 28. Note that the flow velocity and angle ofincidence depend on rotational speed U_(R), which varies along the spanof each blade airfoil 50.

The Zweifel lift coefficient (or Zweifel number) is a dimensionlessratio between the actual and ideal load on blade airfoils 50, and isgiven by:

$\begin{matrix}{{{Zweifel}\mspace{14mu}{Number}} = {\frac{1}{g}{\frac{\overset{.}{m}\;\Delta\;{Cu}}{\frac{1}{2}\rho\; W_{2}^{2}B_{x}h}.}}} & \lbrack 1\rbrack\end{matrix}$In this expression, g is the local gravitational constant oracceleration due to gravity, approximately 32.2 feet per second squared(ft/s²) or 9.81 m/s². The mass flow rate ({dot over (m)}) is giveneither in pounds-mass/second (lbm/s) or kilograms/second (kg/s), andfluid density ρ is expressed in lbm-s²/ft⁴ or kg/m³.

Speeds are typically given in feet/second (ft/s) or meters/second (m/s),where the axial cord length (B_(X)) and span height (h) are measured infeet (ft) or meters (m), respectively. The relative exit velocity is W₂,and the change in tangential velocity across the blade is ΔC_(u):ΔCu=C _(u1) −C _(u2).  [2]

The Zweifel number depends upon the detailed geometry of airfoils 50 andthe adjacent surfaces of turbine blades 28, including the bladeplatform. Low loss blades have Zweifel number greater than one, forexample in the range of 1.10 and above, imparting greater rotationalenergy to the turbine and reducing the number of individual blades 28required for each turbine stage. Suitable blade designs also minimizeweight penalties and reduce the need for cooling fluid flow, providestress resistance and dynamic stability at high temperatures androtational speeds, and limit shock wave losses in transonic flow.

Engine performance also depends on upstream flow conditioning, andturbine vanes 26 are subject to related design considerations. Inparticular, suitable vane airfoils 44 and adjacent platform and shroudsurfaces are shaped to generate efficient turning and acceleration whileminimizing pressure and shock losses. Turbine vanes 26 also emphasizedesigns with lower weight and reduced cooling fluid needs, whileproviding efficient, reliable performance across a range of differentturbine operating conditions.

FIG. 6A is a stacking section view of turbine vane 26. Vane sectionsT1-T7 are distributed at one sixth intervals along the span of airfoil44, from minimum span proximate platform 46 (root or ID section T1) tofull span proximate shroud 48 (tip or OD section T7, at height h).

Platform 46 is attached to vane airfoil 44 at root section T1, formingpart of the inner diameter (ID) flowpath corresponding to inner vanering 40 as shown in FIG. 3A. Shroud 48 is attached at tip section 7,forming part of the outer diameter (OD) flowpath corresponding to outerring 42. The inner flow ring is thus formed at approximately the rootheight or root radius (R_(root)), and the outer flow ring is formed atapproximately the root radius plus the span height (R_(root)+h).

FIG. 6B is a sectional view of turbine rotor blade 28. Blade sectionsS1-S17 are distributed at one sixteenth intervals along the span ofairfoil 50, from minimum span proximate platform 52 (ID or root sectionS1) to maximum span proximate tip 54 (OD or tip section S17). Platform52 is attached to blade airfoil 50 at root section S1, forming part ofthe inner flowpath. Airfoil tip 54 is positioned in rotational clearancewith respect casing 56, along the outer flowpath.

Blade and vane sections T1-T7 and S1-S17 extend along the axial chordsof airfoils 44 and 50, with normalized chord lengths and two-dimensionaloffsets (or displacements) given in Tables 1 and 2, respectively. Thecorresponding fractional spans (S) are normalized to full span height h:

$\begin{matrix}{{S = \frac{Z - Z_{root}}{h}},} & \lbrack 3\rbrack\end{matrix}$where Z is the z coordinate (or height) of the given sectional line andZ_(root) is the z coordinate of the ID or root airfoil section, forexample root vane section T1 or root blade section S1. Full span heighth is defined between the root and the tip:h=Z _(tip) −Z _(root),  [4]where Z_(tip) is the z coordinate of the OD or tip section, for exampleouter (tip) vane section T7 or outer blade section S17.

Chord lengths B_(X) are measured along the axial direction andnormalized according to root chord length B_(Xroot), as defined for theinnermost (root) section:

$\begin{matrix}{\frac{B_{X}}{B_{Xroot}} = {\frac{X_{\max} - X_{\min}}{{X_{\max}\left( Z_{root} \right)} - {X_{\min}\left( Z_{root} \right)}}.}} & \lbrack 5\rbrack\end{matrix}$Stacking lines S_(L) extend through the center of gravity of sectionsT1-T7 and S1-S17, respectively. Two-dimensional stacking offsets ΔX andΔY are determined by the position of the leading edge (X_(LE)) relativeto the blade root, and normalized by the root axial chord length:

$\begin{matrix}{\frac{\Delta\; X}{B_{Xroot}} = {\frac{X_{LE} - {X_{LE}\left( Z_{root} \right)}}{{X_{\max}\left( Z_{root} \right)} - {X_{\min}\left( Z_{root} \right)}}.}} & \lbrack 6\rbrack\end{matrix}$The y-axis is directed in a generally circumferential direction, and yoffsets ΔY are normalized by root pitch τ_(root) (that is, thetangential blade arc at the root). Note that the root pitch depends onthe number of airfoils (N):

$\begin{matrix}{\frac{\Delta\; Y}{\tau_{root}} = {\frac{Y_{LE} - {Y_{LE}\left( Z_{root} \right)}}{2\pi\;{Z_{root}/N}}.}} & \lbrack 7\rbrack\end{matrix}$

FIG. 7 is a cross sectional view of representative airfoil sections 90,92, 94, 96 and 98, for example any of sections T1-T7 of vane airfoil 44(FIG. 6A), or sections S1-S17 of blade airfoil 50 (FIG. 6B). Both the xand y dimensions are normalized by axial chord length B_(x), as definedfor each individual airfoil section. Sections 90, 92, 94, 96 and 98 thusextend from a leading edge region with normalized x coordinate X/B_(X)approaching zero, to a trailing edge region with normalized x coordinateX/B_(X) approaching one.

Normalized y coordinates Y/B_(X) are also given in terms of the axialchord, but the y coordinates are not limited to the leading and trailingedge and vary over a different range. In the representative airfoilsections of FIG. 7, for example, normalized y coordinates Y/B_(X) rangefrom of about −1.2 to about +1.3. Alternatively, normalized ycoordinates Y/B_(X) vary across a range of about ±1.0 or less, or about±2.5 or more.

Airfoil sections are defined by sets of normalized Cartesian coordinatepairs X/B_(X) and Y/B_(X), which are provided for vane and bladeairfoils in Tables 3 and 4, respectively. The Cartesian coordinatesdefine points on a cold, uncoated, stationary airfoil surface, in aplane of constant z. Additional elements such as cooling holes,protective coatings, fillets and seal structures may also be formed ontothe specified airfoil surface, or onto an adjacent platform or shroudsurface, but these elements are not necessarily described by thenormalized coordinates.

Each airfoil section is normalized to its own axial chord length B_(X).The z coordinate is determined by the corresponding fractional span S,from Tables 1 and 2. For each section the x and y coordinates start atthe leading edge, traverse the convex surface clockwise to the trailingedge, and continue across the concave surface back to the leading edge.Three dimensional airfoil surfaces are formed by joining adjacent pointsin Tables 3 and 4 in a smooth manner along the corresponding z plane,and joining adjacent sections along the span.

In general, the blade and vane airfoils described here have acombination of axial sweep and tangential lean. Depending on embodiment,the lean and sweep angles sometimes vary by up to ±5°±10°, ±25°, ormore. In addition, the airfoils are sometimes rotated with respect to aradial axis or a normal to the platform or shroud surface, for exampleby up to ±5°, ±10° or ±25°, or more.

Airfoil surfaces are scaled to a particular size or absolute dimensionby fixing the fractional span and normalized axial chord tocorresponding physical dimensions of the turbine system, along with thenormalized displacements and the normalized Cartesian coordinates. Inparticular, the root axial chord (B_(Xroot)) determines the absolutechord length (B_(X)) from the normalized axial chords (B_(X)/B_(Xroot)),and the chord length determines the absolute airfoil coordinates (X andY) from the normalized coordinates (X/B_(X) and Y/B_(X), respectively).The chord length also determines the absolute x offsets (ΔX) from thecorresponding normalized values (ΔX/B_(X)), and the root pitch(τ_(root)) determines the absolute y offsets (ΔY) from the normalized yvalues (ΔY/τ_(root)).

Normalized axial chords and offsets are given for blades and vanes inTables 1 and 2, respectively, with normalized Cartesian coordinates inTables 3 and 4. To obtain absolute x coordinates, the Cartesiancoordinates and offsets are both scaled to the root axial chord:

$\begin{matrix}{X_{({abs})} = {{\left( \frac{X}{B_{X}} \right)\left( \frac{B_{X}}{B_{Xroot}} \right)B_{Xroot}} + {\left( \frac{\Delta\; X}{B_{Xroot}} \right){B_{Xroot}.}}}} & \lbrack 8\rbrack\end{matrix}$For y coordinates, the displacements are scaled by the root pitch:

$\begin{matrix}{Y_{({abs})} = {{\left( \frac{Y}{B_{X}} \right)\left( \frac{B_{X}}{B_{Xroot}} \right)B_{Xroot}} + {\left( \frac{\Delta\; Y}{\tau_{root}} \right){\tau_{root}.}}}} & \lbrack 9\rbrack\end{matrix}$

The z position (height) is given by scaling the fractional span to thespan height:Z=hS+Z _(root).  [10]This fixes the spacing between successive cross sections, and determinesthe relative height (Z) of each set of airfoil coordinates (X,Y), asdefined along the exterior surface of the vane or blade. The absoluteradial height is based on the height of the root section:R _((abs)) =hS+R _(root),  [11]where the root radius (R_(root)) is measured from the turbine axis.

The root radius and span height vary among different blade and vaneairfoils, as do the root axial chord and pitch. In one set ofembodiments, root chord length B_(Xroot) varies from about three eighthsinch to about two inches, for example about 0.375 inches (9.5 mm), about0.5 inches (12.7 mm), about 0.75 inches (19.1 mm), about 1.0 inches(25.4 mm), about 1.5 inches (38.1 mm) or about 2.0 inches (50.8 mm), orwithin ranges therebetween. Root pitch τ_(root) varies from about onehalf inch to about two and one half inches, for example about 0.5 inches(12.7 mm), about 1.0 inches (25.4 mm), about 1.5 inches (38.1 mm), about2.0 inches (50.8 m) or about 2.5 inches (63.5 mm), or within rangestherebetween. Span height h varies from about one half inch to aboutthree inches, for example about 0.5 inches (12.7 mm), about 1.0 inches(25.4 mm), about 1.5 inches (38.1 mm), about 2.0 inches (50.8 m), about2.5 inches (63.5 mm) or about 3.0 inches (76.2 mm), or within rangestherebetween. Root radius R_(root) varies from about three to abouttwelve inches, for example about 3.0 inches (76 mm), about 4.0 inches(102 mm), about 6.0 inches (152 mm), about 8.0 inches (203 mm) or about12.0 inches (305 mm), or within ranges therebetween.

In one turbine vane embodiment, root chord B_(Xroot) is about 0.98±0.05inches (24.9±1.3 mm), root pitch τ_(root) is about 1.34±0.05 inches(34.0±1.3 mm), span height h is about 1.38±0.05 inches (35.1±1.3 mm),and root radius R_(root) is about 6.80±0.10 inches (172.7±2.5 mm). Inone turbine blade embodiment, root chord B_(Xroot) is about 0.74±0.05inches (18.8±1.3 mm), root pitch τ_(root) is about 0.96±0.05 inches(24.4±1.3 mm), span height h is about 1.56±0.05 inches (39.6±1.3 mm),and root radius R_(root) is about 6.70±0.10 inches (170.2±2.5 mm).

Novel aspects of the blade, vane and airfoil surfaces described hereinare achieved by substantial conformance to specified geometries.Substantial conformance generally includes or may include amanufacturing tolerance of about ±0.050 inches (±1.27 mm), in order toaccount for variations in molding, cutting, shaping, surface finishingand other manufacturing processes, and to accommodate variability incoating thicknesses. This tolerance is absolute, and applies to each ofthe specified airfoil, blade and vane surfaces, regardless of size.

In particular, the manufacturing tolerance is applicable to blade, vaneand airfoil surfaces having a particular size and shape, as determinedby selecting particular scaling parameters (e.g., B_(Xroot), τ_(root), hand R_(root)) from within a specified range, and to non-dimensional(normalized) blade, vane and airfoil surfaces, which are scalable todifferent sizes and shapes within that range. In these embodiments,substantial conformance is based on sets of points representing athree-dimensional surface with particular physical dimensions, forexample in inches or millimeters, as determined by selecting particularvalues of the scaling parameters. A substantially conforming airfoil,blade or vane structure has surfaces that conform to the specified setsof points, within the specified tolerance.

Alternatively, substantial conformance is based on a determination by anational or international regulatory body, for example in a partcertification or part manufacture approval (PMA) process for the FederalAviation Administration, the European Aviation Safety Agency, the CivilAviation Administration of China, the Japan Civil Aviation Bureau, orthe Russian Federal Agency for Air Transport. In these embodiments,substantial conformance encompasses a determination that a particularpart or structure is identical to, or sufficiently similar to, thespecified airfoil, blade or vane, or that the part or structure issufficiently the same with respect to a part design in a type-certifiedor type-certificated airfoil, blade or vane, such that the part orstructure complies with airworthiness standards applicable to thespecified blade, vane or airfoil. In particular, substantial conformanceencompasses any regulatory determination that a particular part orstructure is sufficiently similar to, identical to, or the same as aspecified blade, vane or airfoil, such that certification orauthorization for use is based at least in part on the determination ofsimilarity.

Inner (ID) and outer (OD) flowpath coordinates for turbine vaneplatforms and shrouds are provided in Table 5, with corresponding IDcoordinates for turbine blade platforms are given in Table 6. For theturbine vanes of Table 5, the ID (platform) and OD (shroud) surfaces arerotationally symmetric about the turbine axis, with the curves ofrotation defined according to the platform and shroud coordinates setforth in Table 5. For the turbine blades of Table 6, ID (platform)coordinates are given in three dimensions.

For both blades and vanes, the specified surfaces represent cold,uncoated and stationary inner and outer flowpath surfaces, withoutcooling holes, protective coatings, fillets, seals and other structuresthat may be added during the manufacturing process. The manufacturingtolerance is about ±0.050 inches (±1.27 mm), with substantialconformance to the specified geometry as described above for thecorresponding airfoil surfaces of Tables 1-4.

The inner and outer flowpaths for turbine vanes are given in terms axial(x) coordinates X_(ID) and X_(OD) at corresponding fractional spans S,with rotational coordinate y defined to be zero. That is:

$\begin{matrix}{{S_{ID} = \frac{Z_{ID} - Z_{root}}{h}}{and}} & \lbrack 12\rbrack \\{{S_{OD} = \frac{Z_{OD} - Z_{root}}{h}},} & \lbrack 13\rbrack\end{matrix}$where z coordinates Z_(ID) and Z_(OD) define the platform and shroudsurfaces, respectfully. The x coordinates are normalized by the rootchord, and defined with respect to the leading edge at the root,X_(LE)(Z_(root)). Thus

$\begin{matrix}{{\frac{X_{ID}}{B_{Xroot}} = \frac{X - {X_{LE}\left( Z_{root} \right)}}{{X_{\max}\left( Z_{root} \right)} - {X_{\min}\left( Z_{root} \right)}}}{and}} & \lbrack 14\rbrack \\{\frac{X_{OD}}{B_{Xroot}} = {\frac{X - {X_{LE}\left( Z_{root} \right)}}{{X_{\max}\left( Z_{root} \right)} - {X_{\min}\left( Z_{root} \right)}}.}} & \lbrack 15\rbrack\end{matrix}$

The coordinates in Table 5 extend axially along a smooth curve startingin front of the leading edge and ending behind the trailing edge. Thesurfaces are generated by rotating the curves about the turbine axis toform an annular, axially symmetric flow duct. Thus the inner boundary isdescribed by a curve of rotation defined along or in accordance withplatform coordinates X_(ID) and Z_(ID), and the outer boundary isdescribed by a curve of rotation along or in accordance with shroudcoordinates X_(OD) and Z_(OD).

The inner and outer vane rings are scaled to absolute dimensions usingthe corresponding normalization constants. Thus:

$\begin{matrix}{{X_{{ID}{({abs})}} = {\frac{X_{ID}}{B_{Xroot}}B_{Xroot}}},} & \lbrack 16\rbrack\end{matrix}$where there is no offset because the surface is already defined in termsof the root leading edge. The Z position isZ _(ID) =hS _(ID) +Z _(root),  [17]and the absolute radius of rotation for each point on the curve isR _(ID(abs)) =hS _(ID) +R _(root).  [18]

The outer flowpath is defined by substituting for Z_(ID) and S_(ID):Z _(OD) =hS _(OD) +Z _(root);  [19]R _(OD(abs)) =hS _(OD) +R _(root).  [20]The ID flowpath (S≈0) is thus formed by rotation of the platform curveabout the turbine axis at approximately the root radius, and the ODflowpath (S≈1) is formed by rotation of the shroud curve atapproximately the root radius plus the span height.

For turbine blades, the inner diameter flow surface is defined insubstantial accordance with three-dimensional platform coordinatesX_(P), Y_(P) and Z_(P), as set forth in Table 6. The x coordinates arescaled by the root chord and measured from the root leading edge:

$\begin{matrix}{\frac{X_{P}}{B_{Xroot}} = {\frac{X - {X_{LE}\left( Z_{root} \right)}}{{X_{\max}\left( Z_{root} \right)} - {X_{\min}\left( Z_{root} \right)}}.}} & \lbrack 21\rbrack\end{matrix}$The y coordinates are scaled by the root pitch:

$\begin{matrix}{{\frac{Y_{P}}{\tau_{root}} = \frac{Y - {Y_{LE}\left( Z_{root} \right)}}{2\pi\;{Z_{root}/N}}},} & \lbrack 22\rbrack\end{matrix}$and the z coordinate or height is determined from the correspondingfractional span on the platform surface (Sp):

$\begin{matrix}{S_{P} = {\frac{Z_{P} - Z_{root}}{h}.}} & \lbrack 23\rbrack\end{matrix}$

Absolute x and z coordinates are determined similarly for both vane andblade platforms:

$\begin{matrix}{{X_{P{({abs})}} = {\frac{X_{P}}{B_{Xroot}}B_{Xroot}}};} & \lbrack 24\rbrack \\{Z_{P} = {{hS}_{P} + {Z_{root}.}}} & \lbrack 25\rbrack\end{matrix}$The absolute radial height isR _(P(abs)) =hS _(P) +R _(root),  [26]and the absolute y coordinate is determined from root pitch τ_(root):

$\begin{matrix}{Y_{P{({abs})}} = {\left( \frac{Y_{P}}{\tau_{root}} \right){\tau_{root}.}}} & \lbrack 27\rbrack\end{matrix}$Again, there is no offset term because the platform and shroud surfacesare already measured from the leading edge of the root section, wherethe offset is defined to be zero.

In general, the platform and shroud surfaces are curved in order toprovide converging or diverging flow. Thus the fractional span valuesvary slightly about S=0 along the ID curve, and about S=1 along the ODcurve. In some axial positions, the flow rings extend above or below theroot (ID) and tip (OD) blade sections, corresponding to fractional spanvalues that are less than zero or greater than one, respectively.

TABLE 1 Normalized Axial Chord and Offset (Vane Airfoils) Tolerance:±0.05″ (±1.27 mm) Vane Fractional Axial Chord X offset Y offset SectionSpan (S) B_(X)/B_(Xroot) ΔX/B_(Xroot) ΔY/τ_(root) T1 0.0000 1.00000.00000 0.00000 T2 0.1667 0.9732 0.03970 −0.01068 T3 0.3333 0.98380.03970 −0.01074 T4 0.5000 0.9894 0.03970 −0.01085 T5 0.6667 0.98990.03970 −0.01090 T6 0.8333 0.9855 0.03970 −0.01089 T7 1.0000 1.01300.03972 −0.01085

TABLE 2 Normalized Axial Chord and Offset (Blade Airfoils) Tolerance:±0.05″ (±1.27 mm) Blade Fractional Axial Chord X offset Y offset SectionSpan (S) B_(X)/B_(Xroot) ΔX/B_(Xroot) ΔY/τ_(root) S1 0.0000 1.00000.0000 0.0000 S2 0.0625 0.9721 0.0397 −0.0107 S3 0.1250 0.9458 0.0397−0.0107 S4 0.1875 0.9209 0.0397 −0.0108 S5 0.2500 0.8976 0.0397 −0.0109S6 0.3125 0.8758 0.0397 −0.0109 S7 0.3750 0.8554 0.0397 −0.0108 S80.4375 0.8361 0.0000 0.0000 S9 0.5000 0.8178 0.0397 −0.0107 S10 0.56250.8007 0.0397 −0.0107 S11 0.6250 0.7841 0.0397 −0.0108 S12 0.6875 0.76760.0397 −0.0109 S13 0.7500 0.7511 0.0397 −0.0109 S14 0.8125 0.7343 0.0397−0.0108 S15 0.8750 0.7173 0.0000 0.0000 S16 0.9375 0.7005 0.0397 −0.0107S17 1.0000 0.6838 0.0397 −0.0107

TABLE 3 Normalized Coordinates (Vane Airfoils) Tolerance: ±0.05″ (±1.27mm) Section T1 Section T2 Section T3 Section T4 X/B_(X) Y/B_(X) X/B_(X)Y/B_(X) X/B_(X) Y/B_(X) X/B_(X) Y/B_(X) 0.0000 −0.2735 0.0000 −0.29590.0000 −0.2928 0.0000 −0.2913 0.0001 −0.2669 0.0000 −0.2942 0.0000−0.2910 0.0000 −0.2895 0.0003 −0.2587 0.0000 −0.2925 0.0000 −0.28920.0000 −0.2877 0.0008 −0.2472 0.0001 −0.2890 0.0001 −0.2857 0.0001−0.2841 0.0021 −0.2325 0.0002 −0.2855 0.0002 −0.2821 0.0003 −0.28050.0043 −0.2146 0.0005 −0.2803 0.0005 −0.2768 0.0006 −0.2751 0.0080−0.1936 0.0010 −0.2734 0.0011 −0.2697 0.0011 −0.2679 0.0138 −0.16970.0019 −0.2647 0.0021 −0.2608 0.0022 −0.2590 0.0226 −0.1432 0.0036−0.2527 0.0040 −0.2485 0.0042 −0.2465 0.0350 −0.1145 0.0067 −0.23730.0074 −0.2328 0.0077 −0.2307 0.0511 −0.0841 0.0117 −0.2188 0.0129−0.2140 0.0135 −0.2117 0.0718 −0.0525 0.0192 −0.1975 0.0213 −0.19240.0223 −0.1900 0.0971 −0.0202 0.0302 −0.1739 0.0335 −0.1686 0.0350−0.1662 0.1266 0.0106 0.0455 −0.1485 0.0502 −0.1434 0.0524 −0.14100.1610 0.0411 0.0658 −0.1224 0.0725 −0.1179 0.0757 −0.1158 0.1968 0.07240.0916 −0.0966 0.1006 −0.0931 0.1048 −0.0917 0.2326 0.1038 0.1219−0.0705 0.1325 −0.0674 0.1377 −0.0665 0.2696 0.1363 0.1556 −0.04310.1668 −0.0390 0.1723 −0.0376 0.3063 0.1692 0.1905 −0.0143 0.2019−0.0088 0.2073 −0.0065 0.3425 0.2025 0.2274 0.0176 0.2388 0.0248 0.24390.0282 0.3784 0.2362 0.2648 0.0514 0.2761 0.0606 0.2809 0.0651 0.41410.2701 0.3015 0.0859 0.3126 0.0972 0.3169 0.1030 0.4499 0.3039 0.33880.1225 0.3494 0.1359 0.3532 0.1430 0.4861 0.3373 0.3753 0.1597 0.38550.1754 0.3887 0.1838 0.5227 0.3702 0.4112 0.1976 0.4207 0.2156 0.42340.2253 0.5594 0.4031 0.4463 0.2362 0.4552 0.2564 0.4572 0.2674 0.59520.4368 0.4808 0.2754 0.4889 0.2979 0.4903 0.3101 0.6305 0.4712 0.51450.3152 0.5219 0.3399 0.5228 0.3534 0.6656 0.5058 0.5476 0.3556 0.55420.3825 0.5545 0.3971 0.6999 0.5411 0.5799 0.3965 0.5858 0.4257 0.58550.4414 0.7331 0.5775 0.6115 0.4380 0.6166 0.4694 0.6158 0.4862 0.76380.6138 0.6424 0.4801 0.6467 0.5135 0.6454 0.5314 0.7929 0.6515 0.67250.5227 0.6761 0.5582 0.6744 0.5770 0.8194 0.6890 0.7019 0.5658 0.70480.6033 0.7027 0.6230 0.8427 0.7248 0.7305 0.6095 0.7327 0.6489 0.73030.6695 0.8643 0.7596 0.7582 0.6537 0.7598 0.6950 0.7573 0.7164 0.88350.7921 0.7842 0.6969 0.7853 0.7399 0.7826 0.7621 0.8991 0.8229 0.80940.7406 0.8100 0.7853 0.8073 0.8081 0.9116 0.8514 0.8329 0.7833 0.83310.8295 0.8305 0.8530 0.9225 0.8771 0.8539 0.8233 0.8538 0.8710 0.85130.8949 0.9315 0.9000 0.8735 0.8621 0.8732 0.9111 0.8709 0.9355 0.93890.9200 0.8907 0.8982 0.8903 0.9483 0.8883 0.9731 0.9455 0.9369 0.90420.9322 0.9037 0.9833 0.9019 1.0084 0.9509 0.9506 0.9153 0.9633 0.91481.0152 0.9133 1.0407 0.9563 0.9608 0.9251 0.9912 0.9246 1.0439 0.92341.0696 0.9617 0.9671 0.9333 1.0160 0.9328 1.0693 0.9319 1.0952 0.96720.9708 0.9400 1.0376 0.9396 1.0915 0.9389 1.1176 0.9719 0.9726 0.94601.0557 0.9458 1.1101 0.9453 1.1364 0.9752 0.9732 0.9510 1.0706 0.95081.1253 0.9505 1.1516 0.9786 0.9733 0.9559 1.0818 0.9556 1.1369 0.95541.1634 0.9802 0.9732 0.9611 1.0889 0.9607 1.1444 0.9604 1.1711 0.98190.9729 0.9667 1.0930 0.9662 1.1488 0.9660 1.1756 0.9840 0.9722 0.97171.0947 0.9713 1.1507 0.9711 1.1776 0.9861 0.9713 0.9753 1.0952 0.97491.1513 0.9748 1.1782 0.9901 0.9689 0.9789 1.0951 0.9786 1.1513 0.97851.1781 0.9935 0.9656 0.9807 1.0949 0.9805 1.1511 0.9804 1.1779 0.99740.9599 0.9824 1.0944 0.9823 1.1507 0.9822 1.1775 1.0000 0.9512 0.98471.0937 0.9846 1.1499 0.9846 1.1767 1.0000 0.9399 0.9869 1.0926 0.98681.1488 0.9868 1.1757 0.9978 0.9242 0.9909 1.0899 0.9910 1.1461 0.99101.1729 0.9942 0.9044 0.9944 1.0865 0.9945 1.1426 0.9946 1.1694 0.98920.8802 0.9982 1.0804 0.9983 1.1364 0.9984 1.1632 0.9831 0.8517 1.00001.0714 1.0000 1.1272 1.0000 1.1539 0.9762 0.8188 0.9989 1.0596 0.99871.1152 0.9985 1.1419 0.9689 0.7813 0.9960 1.0434 0.9959 1.0987 0.99571.1252 0.9629 0.7391 0.9922 1.0229 0.9923 1.0779 0.9922 1.1042 0.95690.6924 0.9865 0.9980 0.9868 1.0524 0.9867 1.0785 0.9499 0.6413 0.97970.9685 0.9804 1.0223 0.9804 1.0482 0.9421 0.5857 0.9718 0.9345 0.97270.9877 0.9727 1.0133 0.9337 0.5280 0.9630 0.8960 0.9642 0.9484 0.96440.9737 0.9241 0.4659 0.9548 0.8526 0.9564 0.9042 0.9567 0.9291 0.91340.4017 0.9466 0.8044 0.9486 0.8551 0.9489 0.8796 0.9016 0.3377 0.93700.7518 0.9395 0.8015 0.9400 0.8256 0.8882 0.2718 0.9264 0.6946 0.92930.7432 0.9299 0.7669 0.8732 0.2062 0.9148 0.6353 0.9182 0.6827 0.91900.7059 0.8563 0.1410 0.9019 0.5714 0.9057 0.6177 0.9067 0.6403 0.83720.0765 0.8877 0.5055 0.8920 0.5505 0.8932 0.5725 0.8157 0.0127 0.87290.4397 0.8776 0.4834 0.8790 0.5049 0.7916 −0.0501 0.8566 0.3719 0.86190.4142 0.8634 0.4352 0.7646 −0.1118 0.8394 0.3043 0.8451 0.3453 0.84690.3656 0.7348 −0.1721 0.8210 0.2369 0.8274 0.2766 0.8293 0.2963 0.7020−0.2309 0.8015 0.1699 0.8084 0.2082 0.8105 0.2274 0.6663 −0.2880 0.78060.1034 0.7880 0.1402 0.7905 0.1588 0.6275 −0.3430 0.7581 0.0373 0.76620.0727 0.7689 0.0906 0.5851 −0.3952 0.7339 −0.0281 0.7426 0.0058 0.74570.0230 0.5384 −0.4437 0.7077 −0.0928 0.7171 −0.0604 0.7205 −0.04390.4868 −0.4868 0.6792 −0.1564 0.6893 −0.1257 0.6931 −0.1099 0.4314−0.5209 0.6480 −0.2189 0.6589 −0.1898 0.6632 −0.1748 0.3708 −0.54440.6139 −0.2797 0.6256 −0.2524 0.6303 −0.2383 0.3091 −0.5560 0.5763−0.3385 0.5888 −0.3131 0.5941 −0.2999 0.2508 −0.5558 0.5347 −0.39450.5480 −0.3712 0.5538 −0.3590 0.1962 −0.5429 0.4884 −0.4467 0.5024−0.4255 0.5087 −0.4144 0.1493 −0.5216 0.4383 −0.4918 0.4529 −0.47290.4595 −0.4629 0.1096 −0.4962 0.3822 −0.5292 0.3971 −0.5127 0.4039−0.5039 0.0769 −0.4688 0.3221 −0.5541 0.3368 −0.5401 0.3437 −0.53250.0511 −0.4407 0.2624 −0.5632 0.2765 −0.5516 0.2832 −0.5453 0.0320−0.4130 0.2047 −0.5565 0.2176 −0.5474 0.2237 −0.5424 0.0187 −0.38700.1546 −0.5378 0.1658 −0.5309 0.1712 −0.5271 0.0107 −0.3637 0.1130−0.5123 0.1220 −0.5074 0.1264 −0.5046 0.0063 −0.3440 0.0791 −0.48380.0860 −0.4805 0.0893 −0.4787 0.0038 −0.3285 0.0529 −0.4542 0.0577−0.4520 0.0600 −0.4507 0.0024 −0.3173 0.0338 −0.4250 0.0369 −0.42320.0385 −0.4221 0.0016 −0.3084 0.0205 −0.3979 0.0224 −0.3961 0.0234−0.3951 0.0010 −0.3017 0.0117 −0.3739 0.0129 −0.3719 0.0135 −0.37090.0007 −0.2972 0.0063 −0.3536 0.0070 −0.3514 0.0073 −0.3503 0.0005−0.2927 0.0033 −0.3376 0.0036 −0.3352 0.0038 −0.3340 0.0004 −0.29050.0017 −0.3261 0.0019 −0.3235 0.0020 −0.3222 0.0003 −0.2882 0.0008−0.3169 0.0009 −0.3141 0.0010 −0.3127 0.0002 −0.2866 0.0003 −0.30990.0004 −0.3070 0.0004 −0.3056 0.0002 −0.2850 0.0001 −0.3052 0.0002−0.3023 0.0002 −0.3008 0.0001 −0.2817 0.0000 −0.3006 0.0000 −0.29750.0000 −0.2961 0.0000 −0.2784 0.0000 −0.2983 0.0000 −0.2952 0.0000−0.2937 Section T5 Section T6 Section T7 X/B_(X) Y/B_(X) X/B_(X) Y/B_(X)X/B_(X) Y/B_(X) 0.0000 −0.2913 0.0000 −0.2925 0.0000 −0.2845 0.0000−0.2895 0.0000 −0.2907 0.0000 −0.2828 0.0000 −0.2877 0.0000 −0.28900.0000 −0.2810 0.0001 −0.2841 0.0001 −0.2854 0.0001 −0.2775 0.0002−0.2805 0.0002 −0.2819 0.0002 −0.2740 0.0005 −0.2751 0.0005 −0.27660.0005 −0.2687 0.0011 −0.2679 0.0011 −0.2695 0.0010 −0.2618 0.0022−0.2590 0.0021 −0.2607 0.0020 −0.2530 0.0042 −0.2465 0.0040 −0.24840.0039 −0.2409 0.0077 −0.2307 0.0074 −0.2328 0.0072 −0.2255 0.0135−0.2118 0.0129 −0.2140 0.0125 −0.2069 0.0222 −0.1901 0.0213 −0.19250.0206 −0.1857 0.0349 −0.1663 0.0335 −0.1688 0.0324 −0.1622 0.0524−0.1412 0.0502 −0.1437 0.0487 −0.1372 0.0756 −0.1160 0.0725 −0.11840.0703 −0.1118 0.1048 −0.0920 0.1008 −0.0942 0.0980 −0.0876 0.1379−0.0673 0.1335 −0.0697 0.1300 −0.0630 0.1725 −0.0385 0.1677 −0.04140.1632 −0.0344 0.2071 −0.0070 0.2016 −0.0101 0.1960 −0.0028 0.24320.0281 0.2368 0.0249 0.2301 0.0325 0.2796 0.0656 0.2723 0.0622 0.26450.0699 0.3149 0.1039 0.3068 0.1004 0.2982 0.1080 0.3506 0.1444 0.34170.1406 0.3322 0.1481 0.3854 0.1857 0.3758 0.1815 0.3657 0.1887 0.41950.2276 0.4092 0.2230 0.3986 0.2297 0.4528 0.2701 0.4419 0.2650 0.43090.2712 0.4854 0.3131 0.4741 0.3074 0.4629 0.3129 0.5173 0.3566 0.50570.3503 0.4944 0.3550 0.5486 0.4005 0.5368 0.3935 0.5255 0.3974 0.57930.4450 0.5673 0.4371 0.5563 0.4401 0.6094 0.4898 0.5974 0.4811 0.58670.4830 0.6388 0.5350 0.6270 0.5254 0.6167 0.5262 0.6677 0.5806 0.65610.5700 0.6464 0.5696 0.6960 0.6266 0.6847 0.6149 0.6757 0.6133 0.72380.6729 0.7129 0.6601 0.7047 0.6571 0.7509 0.7196 0.7406 0.7055 0.73330.7013 0.7765 0.7650 0.7669 0.7498 0.7606 0.7442 0.8016 0.8108 0.79270.7943 0.7871 0.7876 0.8252 0.8553 0.8172 0.8375 0.8114 0.8302 0.84660.8969 0.8396 0.8779 0.8329 0.8704 0.8667 0.9371 0.8607 0.9170 0.85160.9100 0.8847 0.9744 0.8796 0.9531 0.8659 0.9477 0.8990 1.0093 0.89490.9871 0.8780 0.9825 0.9110 1.0414 0.9078 1.0183 0.8878 1.0143 0.92171.0700 0.9192 1.0462 0.8957 1.0430 0.9307 1.0955 0.9290 1.0710 0.90241.0685 0.9381 1.1176 0.9371 1.0926 0.9084 1.0905 0.9449 1.1363 0.94431.1107 0.9152 1.1085 0.9504 1.1514 0.9502 1.1255 0.9233 1.1221 0.95541.1631 0.9555 1.1369 0.9314 1.1313 0.9606 1.1707 0.9609 1.1441 0.93831.1368 0.9662 1.1751 0.9666 1.1483 0.9445 1.1401 0.9713 1.1770 0.97171.1500 0.9496 1.1418 0.9750 1.1775 0.9754 1.1504 0.9531 1.1425 0.97871.1775 0.9790 1.1502 0.9566 1.1428 0.9805 1.1772 0.9809 1.1499 0.95841.1428 0.9824 1.1768 0.9827 1.1495 0.9601 1.1426 0.9847 1.1760 0.98501.1487 0.9624 1.1423 0.9870 1.1749 0.9872 1.1476 0.9647 1.1418 0.99121.1722 0.9914 1.1448 0.9692 1.1403 0.9947 1.1686 0.9949 1.1414 0.97341.1382 0.9984 1.1624 0.9986 1.1352 0.9793 1.1340 1.0000 1.1532 1.00001.1262 0.9858 1.1272 0.9984 1.1412 0.9982 1.1143 0.9919 1.1173 0.99561.1245 0.9952 1.0978 0.9976 1.1019 0.9920 1.1036 0.9914 1.0771 1.00001.0811 0.9864 1.0780 0.9855 1.0519 0.9963 1.0558 0.9799 1.0478 0.97881.0221 0.9878 1.0267 0.9722 1.0129 0.9708 0.9877 0.9768 0.9936 0.96370.9734 0.9620 0.9487 0.9643 0.9560 0.9558 0.9289 0.9536 0.9048 0.95070.9139 0.9479 0.8796 0.9453 0.8561 0.9367 0.8671 0.9388 0.8256 0.93580.8028 0.9239 0.8151 0.9286 0.7671 0.9250 0.7450 0.9105 0.7584 0.91740.7062 0.9135 0.6849 0.8967 0.6994 0.9049 0.6408 0.9005 0.6203 0.88180.6360 0.8913 0.5732 0.8865 0.5535 0.8663 0.5702 0.8770 0.5057 0.87170.4869 0.8504 0.5046 0.8613 0.4361 0.8556 0.4182 0.8336 0.4368 0.84470.3667 0.8386 0.3497 0.8162 0.3692 0.8271 0.2976 0.8206 0.2814 0.79800.3017 0.8082 0.2288 0.8014 0.2135 0.7791 0.2344 0.7881 0.1603 0.78100.1459 0.7590 0.1675 0.7666 0.0923 0.7591 0.0788 0.7376 0.1010 0.74340.0248 0.7357 0.0122 0.7147 0.0350 0.7182 −0.0420 0.7104 −0.0537 0.6901−0.0303 0.6910 −0.1079 0.6830 −0.1187 0.6635 −0.0950 0.6613 −0.17280.6532 −0.1827 0.6347 −0.1586 0.6286 −0.2362 0.6205 −0.2452 0.6032−0.2209 0.5926 −0.2978 0.5845 −0.3059 0.5686 −0.2816 0.5526 −0.35680.5445 −0.3641 0.5301 −0.3399 0.5077 −0.4123 0.4997 −0.4186 0.4872−0.3950 0.4588 −0.4609 0.4510 −0.4664 0.4406 −0.4439 0.4035 −0.50200.3959 −0.5066 0.3880 −0.4861 0.3435 −0.5308 0.3364 −0.5347 0.3307−0.5172 0.2831 −0.5438 0.2765 −0.5470 0.2724 −0.5331 0.2238 −0.54120.2179 −0.5437 0.2142 −0.5329 0.1712 −0.5262 0.1661 −0.5280 0.1625−0.5189 0.1265 −0.5040 0.1222 −0.5053 0.1190 −0.4966 0.0893 −0.47820.0861 −0.4790 0.0836 −0.4700 0.0601 −0.4503 0.0578 −0.4507 0.0561−0.4415 0.0385 −0.4218 0.0371 −0.4221 0.0359 −0.4130 0.0234 −0.39480.0225 −0.3952 0.0218 −0.3862 0.0135 −0.3706 0.0130 −0.3711 0.0126−0.3624 0.0073 −0.3501 0.0070 −0.3508 0.0068 −0.3422 0.0038 −0.33390.0037 −0.3347 0.0035 −0.3263 0.0020 −0.3221 0.0019 −0.3230 0.0018−0.3147 0.0010 −0.3126 0.0009 −0.3137 0.0009 −0.3055 0.0004 −0.30550.0004 −0.3066 0.0004 −0.2985 0.0002 −0.3008 0.0002 −0.3019 0.0002−0.2938 0.0000 −0.2960 0.0000 −0.2972 0.0000 −0.2892 0.0000 −0.29360.0000 −0.2949 0.0000 −0.2868

TABLE 4 Normalized Coordinates (Blade Airfoils) Tolerance: ±0.05″ (±1.27mm) Section S1 Section S2 Section S3 Section S4 X/B_(X) Y/B_(X) X/B_(X)Y/B_(X) X/B_(X) Y/B_(X) X/B_(X) Y/B_(X) 0.0000 0.2403 0.0000 0.25990.0000 0.2832 0.0000 0.3105 0.0019 0.2591 0.0014 0.2791 0.0010 0.30270.0008 0.3303 0.0072 0.2816 0.0061 0.3021 0.0053 0.3262 0.0050 0.35420.0156 0.3076 0.0143 0.3286 0.0135 0.3533 0.0133 0.3817 0.0266 0.33710.0257 0.3586 0.0254 0.3836 0.0256 0.4124 0.0411 0.3697 0.0408 0.39170.0410 0.4171 0.0419 0.4462 0.0602 0.4048 0.0604 0.4272 0.0615 0.45300.0633 0.4823 0.0850 0.4412 0.0861 0.4640 0.0882 0.4899 0.0913 0.51920.1173 0.4771 0.1195 0.5000 0.1229 0.5257 0.1276 0.5544 0.1589 0.50930.1624 0.5319 0.1675 0.5567 0.1743 0.5838 0.2085 0.5319 0.2138 0.55350.2207 0.5764 0.2292 0.6007 0.2664 0.5415 0.2733 0.5607 0.2815 0.58060.2910 0.6014 0.3269 0.5354 0.3346 0.5516 0.3432 0.5684 0.3528 0.58550.3846 0.5161 0.3924 0.5296 0.4009 0.5435 0.4102 0.5575 0.4399 0.48620.4475 0.4972 0.4557 0.5084 0.4643 0.5196 0.4907 0.4490 0.4980 0.45780.5056 0.4666 0.5135 0.4755 0.5372 0.4067 0.5440 0.4134 0.5510 0.42010.5581 0.4268 0.5799 0.3604 0.5862 0.3652 0.5925 0.3700 0.5988 0.37470.6190 0.3111 0.6247 0.3141 0.6303 0.3171 0.6357 0.3199 0.6549 0.25940.6600 0.2607 0.6648 0.2620 0.6694 0.2631 0.6878 0.2058 0.6923 0.20550.6964 0.2051 0.7001 0.2046 0.7181 0.1506 0.7219 0.1488 0.7253 0.14690.7283 0.1449 0.7460 0.0942 0.7492 0.0909 0.7519 0.0875 0.7542 0.08420.7717 0.0367 0.7743 0.0321 0.7765 0.0274 0.7782 0.0226 0.7955 −0.02150.7976 −0.0275 0.7993 −0.0335 0.8005 −0.0396 0.8175 −0.0804 0.8193−0.0877 0.8205 −0.0950 0.8212 −0.1023 0.8381 −0.1399 0.8394 −0.14840.8403 −0.1569 0.8406 −0.1654 0.8573 −0.1998 0.8583 −0.2095 0.8588−0.2192 0.8588 −0.2288 0.8747 −0.2581 0.8754 −0.2689 0.8756 −0.27970.8754 −0.2905 0.8910 −0.3167 0.8915 −0.3286 0.8915 −0.3405 0.8912−0.3523 0.9059 −0.3734 0.9061 −0.3864 0.9060 −0.3994 0.9055 −0.41220.9191 −0.4263 0.9192 −0.4403 0.9190 −0.4542 0.9184 −0.4680 0.9324−0.4770 0.9324 −0.4919 0.9322 −0.5067 0.9316 −0.5214 0.9450 −0.52350.9450 −0.5393 0.9447 −0.5549 0.9442 −0.5703 0.9567 −0.5660 0.9567−0.5824 0.9565 −0.5988 0.9561 −0.6150 0.9668 −0.6045 0.9668 −0.62160.9666 −0.6387 0.9663 −0.6555 0.9755 −0.6391 0.9755 −0.6568 0.9754−0.6744 0.9752 −0.6918 0.9830 −0.6696 0.9830 −0.6878 0.9830 −0.70600.9828 −0.7239 0.9893 −0.6961 0.9894 −0.7148 0.9894 −0.7334 0.9894−0.7518 0.9946 −0.7185 0.9946 −0.7376 0.9947 −0.7566 0.9948 −0.77540.9981 −0.7370 0.9982 −0.7564 0.9984 −0.7757 0.9985 −0.7948 1.0000−0.7516 1.0000 −0.7713 1.0000 −0.7908 1.0000 −0.8101 0.9981 −0.76190.9980 −0.7817 0.9978 −0.8014 0.9976 −0.8208 0.9942 −0.7692 0.9938−0.7892 0.9935 −0.8089 0.9932 −0.8284 0.9900 −0.7739 0.9895 −0.79390.9891 −0.8137 0.9887 −0.8333 0.9867 −0.7766 0.9862 −0.7965 0.9857−0.8164 0.9852 −0.8359 0.9831 −0.7787 0.9825 −0.7987 0.9820 −0.81860.9814 −0.8382 0.9812 −0.7796 0.9806 −0.7996 0.9800 −0.8195 0.9794−0.8391 0.9793 −0.7804 0.9786 −0.8004 0.9780 −0.8203 0.9774 −0.83990.9779 −0.7808 0.9772 −0.8008 0.9766 −0.8207 0.9759 −0.8403 0.9765−0.7811 0.9758 −0.8011 0.9751 −0.8210 0.9744 −0.8406 0.9738 −0.78150.9730 −0.8016 0.9722 −0.8215 0.9714 −0.8411 0.9710 −0.7818 0.9701−0.8018 0.9693 −0.8217 0.9684 −0.8413 0.9668 −0.7816 0.9658 −0.80160.9649 −0.8215 0.9639 −0.8411 0.9613 −0.7805 0.9602 −0.8005 0.9591−0.8203 0.9579 −0.8399 0.9548 −0.7777 0.9536 −0.7976 0.9523 −0.81740.9510 −0.8369 0.9473 −0.7714 0.9459 −0.7912 0.9444 −0.8108 0.9429−0.8300 0.9406 −0.7606 0.9391 −0.7801 0.9375 −0.7995 0.9358 −0.81840.9341 −0.7466 0.9325 −0.7658 0.9307 −0.7847 0.9289 −0.8033 0.9260−0.7303 0.9243 −0.7490 0.9224 −0.7675 0.9205 −0.7855 0.9166 −0.71140.9149 −0.7296 0.9130 −0.7475 0.9110 −0.7649 0.9058 −0.6901 0.9041−0.7077 0.9022 −0.7249 0.9000 −0.7417 0.8935 −0.6665 0.8919 −0.68330.8899 −0.6998 0.8877 −0.7157 0.8798 −0.6403 0.8783 −0.6563 0.8765−0.6719 0.8742 −0.6870 0.8645 −0.6119 0.8633 −0.6269 0.8615 −0.64150.8593 −0.6555 0.8465 −0.5817 0.8456 −0.5956 0.8441 −0.6091 0.8419−0.6220 0.8267 −0.5510 0.8262 −0.5637 0.8249 −0.5759 0.8228 −0.58760.8045 −0.5186 0.8043 −0.5299 0.8033 −0.5408 0.8014 −0.5510 0.7809−0.4854 0.7813 −0.4952 0.7807 −0.5046 0.7790 −0.5133 0.7568 −0.45250.7578 −0.4608 0.7576 −0.4686 0.7562 −0.4758 0.7314 −0.4189 0.7330−0.4256 0.7334 −0.4317 0.7324 −0.4372 0.7054 −0.3857 0.7077 −0.39060.7087 −0.3951 0.7081 −0.3989 0.6789 −0.3529 0.6820 −0.3561 0.6836−0.3587 0.6835 −0.3607 0.6519 −0.3205 0.6557 −0.3219 0.6580 −0.32270.6585 −0.3228 0.6244 −0.2886 0.6290 −0.2881 0.6319 −0.2870 0.6331−0.2852 0.5964 −0.2571 0.6017 −0.2547 0.6054 −0.2516 0.6072 −0.24790.5678 −0.2261 0.5739 −0.2217 0.5783 −0.2167 0.5809 −0.2109 0.5387−0.1956 0.5455 −0.1892 0.5507 −0.1821 0.5540 −0.1743 0.5091 −0.16560.5166 −0.1572 0.5225 −0.1480 0.5266 −0.1381 0.4789 −0.1361 0.4871−0.1257 0.4937 −0.1144 0.4986 −0.1023 0.4482 −0.1073 0.4570 −0.09470.4643 −0.0813 0.4700 −0.0670 0.4169 −0.0790 0.4262 −0.0644 0.4342−0.0488 0.4407 −0.0322 0.3849 −0.0515 0.3948 −0.0348 0.4035 −0.01700.4107 0.0020 0.3523 −0.0248 0.3627 −0.0059 0.3719 0.0141 0.3799 0.03540.3202 0.0003 0.3309 0.0211 0.3406 0.0433 0.3492 0.0668 0.2873 0.02440.2983 0.0472 0.3083 0.0715 0.3174 0.0971 0.2549 0.0467 0.2660 0.07130.2762 0.0974 0.2854 0.1250 0.2242 0.0664 0.2351 0.0924 0.2452 0.12000.2544 0.1493 0.1939 0.0843 0.2044 0.1112 0.2142 0.1400 0.2231 0.17060.1655 0.0996 0.1753 0.1268 0.1844 0.1561 0.1926 0.1874 0.1389 0.11250.1477 0.1391 0.1558 0.1680 0.1631 0.1993 0.1144 0.1231 0.1220 0.14760.1290 0.1749 0.1352 0.2050 0.0921 0.1314 0.0986 0.1538 0.1045 0.17920.1097 0.2078 0.0722 0.1386 0.0779 0.1599 0.0830 0.1844 0.0874 0.21210.0556 0.1462 0.0606 0.1668 0.0649 0.1906 0.0686 0.2178 0.0425 0.15430.0467 0.1743 0.0504 0.1977 0.0534 0.2246 0.0325 0.1621 0.0362 0.18180.0392 0.2049 0.0417 0.2315 0.0255 0.1690 0.0286 0.1884 0.0312 0.21130.0332 0.2379 0.0208 0.1743 0.0236 0.1936 0.0259 0.2164 0.0276 0.24300.0174 0.1788 0.0200 0.1980 0.0220 0.2208 0.0235 0.2474 0.0151 0.18220.0174 0.2015 0.0192 0.2243 0.0205 0.2509 0.0136 0.1846 0.0157 0.20380.0175 0.2266 0.0187 0.2533 0.0122 0.1870 0.0142 0.2063 0.0158 0.22910.0169 0.2557 0.0115 0.1883 0.0134 0.2075 0.0150 0.2303 0.0160 0.25700.0108 0.1895 0.0127 0.2087 0.0142 0.2316 0.0152 0.2582 0.0099 0.19140.0117 0.2106 0.0131 0.2334 0.0140 0.2601 0.0090 0.1933 0.0107 0.21250.0120 0.2353 0.0129 0.2620 0.0073 0.1971 0.0088 0.2163 0.0100 0.23910.0108 0.2659 0.0058 0.2010 0.0071 0.2202 0.0082 0.2431 0.0089 0.26980.0039 0.2070 0.0050 0.2263 0.0058 0.2492 0.0064 0.2759 0.0019 0.21520.0027 0.2345 0.0033 0.2575 0.0037 0.2843 0.0004 0.2256 0.0009 0.24500.0012 0.2681 0.0014 0.2951 0.0000 0.2403 0.0000 0.2599 0.0000 0.28320.0000 0.3105 Section S5 Section S6 Section S7 Section S8 X/B_(X)Y/B_(X) X/B_(X) Y/B_(X) X/B_(X) Y/B_(X) X/B_(X) Y/B_(X) 0.0000 0.34190.0000 0.3775 0.0000 0.4171 0.0000 0.4602 0.0008 0.3620 0.0010 0.39790.0014 0.4377 0.0020 0.4811 0.0050 0.3863 0.0055 0.4225 0.0065 0.46260.0079 0.5061 0.0136 0.4141 0.0145 0.4506 0.0161 0.4908 0.0184 0.53450.0265 0.4451 0.0281 0.4818 0.0305 0.5222 0.0338 0.5659 0.0435 0.47920.0460 0.5160 0.0495 0.5563 0.0542 0.5998 0.0660 0.5153 0.0696 0.55210.0745 0.5921 0.0812 0.6350 0.0954 0.5520 0.1008 0.5883 0.1078 0.62750.1169 0.6687 0.1338 0.5863 0.1416 0.6211 0.1513 0.6580 0.1633 0.69600.1828 0.6133 0.1932 0.6448 0.2055 0.6776 0.2199 0.7104 0.2394 0.62640.2514 0.6534 0.2651 0.6807 0.2803 0.7074 0.3019 0.6228 0.3142 0.64480.3278 0.6666 0.3424 0.6876 0.3636 0.6030 0.3753 0.6207 0.3880 0.63800.4012 0.6544 0.4203 0.5717 0.4311 0.5859 0.4425 0.5997 0.4542 0.61250.4735 0.5310 0.4833 0.5423 0.4933 0.5531 0.5035 0.5629 0.5217 0.48440.5303 0.4931 0.5390 0.5014 0.5477 0.5087 0.5654 0.4335 0.5727 0.44000.5801 0.4460 0.5874 0.4512 0.6050 0.3793 0.6111 0.3838 0.6172 0.38780.6232 0.3911 0.6409 0.3227 0.6459 0.3253 0.6507 0.3275 0.6555 0.32910.6736 0.2642 0.6775 0.2651 0.6813 0.2657 0.6851 0.2658 0.7034 0.20410.7064 0.2035 0.7092 0.2026 0.7121 0.2013 0.7308 0.1429 0.7329 0.14080.7348 0.1385 0.7370 0.1359 0.7560 0.0807 0.7574 0.0773 0.7586 0.07370.7602 0.0700 0.7794 0.0179 0.7801 0.0131 0.7807 0.0084 0.7818 0.00350.8011 −0.0456 0.8012 −0.0515 0.8014 −0.0575 0.8021 −0.0635 0.8214−0.1095 0.8211 −0.1166 0.8208 −0.1237 0.8212 −0.1307 0.8404 −0.17380.8398 −0.1820 0.8392 −0.1902 0.8393 −0.1983 0.8584 −0.2384 0.8574−0.2477 0.8566 −0.2570 0.8565 −0.2660 0.8747 −0.3011 0.8736 −0.31150.8726 −0.3217 0.8725 −0.3317 0.8903 −0.3640 0.8891 −0.3754 0.8880−0.3866 0.8877 −0.3975 0.9046 −0.4249 0.9033 −0.4373 0.9022 −0.44940.9019 −0.4612 0.9174 −0.4815 0.9162 −0.4948 0.9151 −0.5078 0.9148−0.5204 0.9307 −0.5358 0.9296 −0.5499 0.9286 −0.5636 0.9283 −0.57710.9435 −0.5855 0.9425 −0.6004 0.9416 −0.6149 0.9414 −0.6291 0.9555−0.6309 0.9546 −0.6464 0.9540 −0.6616 0.9538 −0.6764 0.9658 −0.67210.9652 −0.6882 0.9647 −0.7039 0.9646 −0.7193 0.9748 −0.7089 0.9744−0.7256 0.9740 −0.7419 0.9740 −0.7578 0.9826 −0.7415 0.9823 −0.75870.9821 −0.7754 0.9822 −0.7918 0.9893 −0.7698 0.9892 −0.7873 0.9891−0.8045 0.9892 −0.8212 0.9948 −0.7937 0.9948 −0.8116 0.9948 −0.82910.9949 −0.8462 0.9986 −0.8134 0.9988 −0.8316 0.9989 −0.8494 0.9991−0.8668 1.0000 −0.8291 1.0000 −0.8475 1.0000 −0.8655 1.0000 −0.88310.9974 −0.8399 0.9972 −0.8584 0.9971 −0.8765 0.9969 −0.8943 0.9929−0.8476 0.9926 −0.8662 0.9922 −0.8844 0.9919 −0.9022 0.9883 −0.85240.9878 −0.8711 0.9874 −0.8893 0.9870 −0.9071 0.9847 −0.8551 0.9842−0.8738 0.9838 −0.8920 0.9833 −0.9099 0.9808 −0.8574 0.9803 −0.87610.9798 −0.8943 0.9792 −0.9122 0.9788 −0.8583 0.9782 −0.8770 0.9777−0.8953 0.9771 −0.9131 0.9767 −0.8591 0.9761 −0.8778 0.9755 −0.89610.9749 −0.9140 0.9752 −0.8595 0.9746 −0.8782 0.9739 −0.8965 0.9733−0.9144 0.9737 −0.8599 0.9730 −0.8786 0.9723 −0.8969 0.9716 −0.91480.9706 −0.8603 0.9698 −0.8791 0.9690 −0.8974 0.9683 −0.9153 0.9675−0.8605 0.9666 −0.8793 0.9657 −0.8975 0.9649 −0.9155 0.9629 −0.86030.9618 −0.8790 0.9608 −0.8973 0.9598 −0.9152 0.9568 −0.8590 0.9556−0.8777 0.9544 −0.8959 0.9531 −0.9137 0.9496 −0.8559 0.9482 −0.87440.9468 −0.8925 0.9454 −0.9101 0.9414 −0.8489 0.9398 −0.8671 0.9382−0.8849 0.9365 −0.9022 0.9341 −0.8369 0.9323 −0.8548 0.9306 −0.87210.9288 −0.8890 0.9271 −0.8213 0.9251 −0.8387 0.9232 −0.8555 0.9213−0.8719 0.9184 −0.8030 0.9163 −0.8199 0.9141 −0.8361 0.9120 −0.85180.9087 −0.7818 0.9063 −0.7980 0.9039 −0.8136 0.9016 −0.8285 0.8976−0.7578 0.8949 −0.7733 0.8922 −0.7881 0.8897 −0.8022 0.8851 −0.73110.8822 −0.7457 0.8792 −0.7595 0.8764 −0.7727 0.8714 −0.7014 0.8683−0.7150 0.8650 −0.7279 0.8621 −0.7400 0.8565 −0.6689 0.8531 −0.68150.8496 −0.6933 0.8464 −0.7042 0.8390 −0.6341 0.8354 −0.6455 0.8316−0.6561 0.8282 −0.6658 0.8198 −0.5985 0.8161 −0.6087 0.8120 −0.61790.8083 −0.6263 0.7984 −0.5606 0.7945 −0.5693 0.7902 −0.5772 0.7863−0.5840 0.7761 −0.5214 0.7721 −0.5286 0.7676 −0.5349 0.7635 −0.54030.7535 −0.4823 0.7495 −0.4880 0.7449 −0.4928 0.7407 −0.4966 0.7299−0.4421 0.7260 −0.4461 0.7214 −0.4492 0.7170 −0.4513 0.7060 −0.40200.7022 −0.4043 0.6977 −0.4057 0.6933 −0.4061 0.6818 −0.3620 0.6783−0.3626 0.6739 −0.3623 0.6696 −0.3609 0.6572 −0.3223 0.6541 −0.32100.6500 −0.3189 0.6458 −0.3158 0.6323 −0.2828 0.6297 −0.2796 0.6259−0.2756 0.6219 −0.2706 0.6071 −0.2435 0.6050 −0.2384 0.6016 −0.23240.5980 −0.2255 0.5814 −0.2045 0.5800 −0.1973 0.5772 −0.1893 0.5740−0.1805 0.5553 −0.1658 0.5547 −0.1564 0.5526 −0.1463 0.5499 −0.13550.5288 −0.1274 0.5290 −0.1158 0.5278 −0.1035 0.5257 −0.0906 0.5017−0.0893 0.5029 −0.0755 0.5025 −0.0609 0.5011 −0.0458 0.4740 −0.05170.4762 −0.0355 0.4768 −0.0187 0.4762 −0.0013 0.4456 −0.0146 0.44880.0040 0.4504 0.0232 0.4506 0.0429 0.4165 0.0220 0.4207 0.0430 0.42330.0646 0.4243 0.0866 0.3865 0.0578 0.3916 0.0812 0.3951 0.1054 0.39700.1297 0.3565 0.0915 0.3624 0.1174 0.3668 0.1439 0.3693 0.1705 0.32520.1241 0.3318 0.1523 0.3369 0.1813 0.3401 0.2103 0.2937 0.1541 0.30070.1846 0.3063 0.2159 0.3099 0.2472 0.2627 0.1803 0.2699 0.2127 0.27570.2460 0.2797 0.2794 0.2311 0.2030 0.2381 0.2371 0.2438 0.2723 0.24780.3077 0.2000 0.2207 0.2065 0.2560 0.2117 0.2926 0.2155 0.3299 0.16960.2329 0.1751 0.2688 0.1796 0.3065 0.1830 0.3452 0.1406 0.2380 0.14510.2738 0.1486 0.3121 0.1514 0.3522 0.1141 0.2398 0.1177 0.2751 0.12040.3133 0.1223 0.3541 0.0911 0.2433 0.0938 0.2780 0.0958 0.3159 0.09700.3565 0.0715 0.2487 0.0736 0.2832 0.0749 0.3210 0.0755 0.3617 0.05570.2552 0.0572 0.2895 0.0579 0.3273 0.0579 0.3682 0.0435 0.2620 0.04450.2963 0.0448 0.3342 0.0443 0.3752 0.0346 0.2684 0.0353 0.3027 0.03530.3407 0.0345 0.3820 0.0287 0.2735 0.0292 0.3079 0.0290 0.3461 0.02810.3875 0.0244 0.2779 0.0246 0.3125 0.0243 0.3507 0.0233 0.3923 0.02130.2814 0.0214 0.3160 0.0210 0.3544 0.0199 0.3962 0.0193 0.2839 0.01940.3185 0.0189 0.3570 0.0178 0.3989 0.0175 0.2864 0.0175 0.3211 0.01700.3597 0.0158 0.4016 0.0166 0.2876 0.0166 0.3224 0.0160 0.3610 0.01490.4030 0.0157 0.2889 0.0157 0.3237 0.0151 0.3624 0.0139 0.4045 0.01450.2908 0.0145 0.3256 0.0139 0.3643 0.0127 0.4065 0.0134 0.2927 0.01330.3276 0.0127 0.3663 0.0116 0.4085 0.0112 0.2966 0.0111 0.3315 0.01050.3703 0.0094 0.4126 0.0092 0.3006 0.0091 0.3356 0.0085 0.3745 0.00750.4169 0.0066 0.3068 0.0065 0.3419 0.0059 0.3809 0.0050 0.4234 0.00380.3153 0.0037 0.3506 0.0033 0.3897 0.0026 0.4324 0.0015 0.3263 0.00140.3617 0.0011 0.4010 0.0007 0.4439 0.0000 0.3419 0.0000 0.3775 0.00000.4171 0.0000 0.4602 Section S9 Section S10 Section S11 X/B_(X) Y/B_(X)X/B_(X) Y/B_(X) X/B_(X) Y/B_(X) 0.0000 0.5065 0.0000 0.5384 0.00000.5906 0.0029 0.5276 0.0007 0.5552 0.0017 0.6076 0.0098 0.5527 0.00460.5765 0.0069 0.6289 0.0215 0.5811 0.0128 0.6016 0.0167 0.6538 0.03820.6124 0.0260 0.6299 0.0317 0.6817 0.0604 0.6460 0.0445 0.6610 0.05230.7121 0.0899 0.6799 0.0691 0.6938 0.0796 0.7436 0.1286 0.7110 0.10160.7259 0.1157 0.7729 0.1779 0.7338 0.1438 0.7531 0.1614 0.7950 0.23630.7419 0.1958 0.7698 0.2157 0.8043 0.2969 0.7324 0.2551 0.7706 0.27510.7971 0.3578 0.7068 0.3149 0.7545 0.3332 0.7743 0.4148 0.6691 0.37400.7233 0.3900 0.7377 0.4660 0.6237 0.4288 0.6811 0.4424 0.6915 0.51350.5712 0.4779 0.6324 0.4892 0.6397 0.5562 0.5147 0.5235 0.5773 0.53280.5819 0.5945 0.4551 0.5645 0.5186 0.5722 0.5212 0.6290 0.3933 0.60150.4572 0.6080 0.4583 0.6604 0.3298 0.6350 0.3940 0.6407 0.3937 0.68910.2651 0.6657 0.3292 0.6708 0.3278 0.7155 0.1994 0.6939 0.2634 0.69860.2610 0.7400 0.1329 0.7199 0.1967 0.7245 0.1934 0.7627 0.0659 0.74410.1293 0.7487 0.1252 0.7840 −0.0016 0.7667 0.0614 0.7713 0.0564 0.8041−0.0696 0.7880 −0.0070 0.7926 −0.0127 0.8230 −0.1378 0.8080 −0.07580.8127 −0.0823 0.8410 −0.2063 0.8268 −0.1448 0.8317 −0.1521 0.8581−0.2750 0.8448 −0.2141 0.8496 −0.2222 0.8739 −0.3415 0.8618 −0.28370.8666 −0.2925 0.8891 −0.4083 0.8775 −0.3511 0.8822 −0.3607 0.9031−0.4728 0.8925 −0.4186 0.8971 −0.4291 0.9158 −0.5328 0.9063 −0.48400.9106 −0.4952 0.9292 −0.5903 0.9188 −0.5447 0.9228 −0.5567 0.9423−0.6430 0.9319 −0.6029 0.9355 −0.6156 0.9546 −0.6909 0.9446 −0.65620.9478 −0.6697 0.9653 −0.7345 0.9567 −0.7049 0.9595 −0.7190 0.9746−0.7735 0.9671 −0.7490 0.9694 −0.7637 0.9827 −0.8079 0.9760 −0.78850.9779 −0.8038 0.9896 −0.8378 0.9837 −0.8235 0.9851 −0.8392 0.9952−0.8631 0.9904 −0.8537 0.9914 −0.8699 0.9993 −0.8840 0.9957 −0.87940.9963 −0.8960 1.0000 −0.9005 0.9995 −0.9005 0.9997 −0.9174 0.9967−0.9118 1.0000 −0.9173 1.0000 −0.9343 0.9916 −0.9197 0.9966 −0.92860.9964 −0.9457 0.9867 −0.9247 0.9914 −0.9366 0.9911 −0.9538 0.9828−0.9275 0.9863 −0.9417 0.9859 −0.9588 0.9787 −0.9298 0.9824 −0.94450.9820 −0.9617 0.9766 −0.9308 0.9783 −0.9468 0.9778 −0.9640 0.9744−0.9316 0.9761 −0.9477 0.9756 −0.9650 0.9727 −0.9321 0.9738 −0.94860.9733 −0.9658 0.9710 −0.9324 0.9721 −0.9490 0.9715 −0.9663 0.9675−0.9330 0.9703 −0.9494 0.9697 −0.9666 0.9640 −0.9331 0.9668 −0.94990.9660 −0.9672 0.9587 −0.9328 0.9632 −0.9501 0.9623 −0.9674 0.9519−0.9312 0.9578 −0.9498 0.9568 −0.9670 0.9440 −0.9275 0.9507 −0.94810.9495 −0.9652 0.9349 −0.9193 0.9426 −0.9442 0.9412 −0.9612 0.9271−0.9056 0.9333 −0.9357 0.9317 −0.9523 0.9195 −0.8879 0.9255 −0.92150.9239 −0.9375 0.9101 −0.8671 0.9179 −0.9031 0.9164 −0.9185 0.8996−0.8430 0.9086 −0.8816 0.9072 −0.8962 0.8876 −0.8158 0.8982 −0.85670.8969 −0.8703 0.8743 −0.7853 0.8863 −0.8285 0.8852 −0.8410 0.8598−0.7515 0.8730 −0.7969 0.8721 −0.8083 0.8440 −0.7144 0.8586 −0.76190.8579 −0.7720 0.8257 −0.6746 0.8429 −0.7235 0.8423 −0.7322 0.8057−0.6337 0.8247 −0.6823 0.8243 −0.6895 0.7835 −0.5899 0.8047 −0.63980.8044 −0.6454 0.7606 −0.5446 0.7826 −0.5945 0.7823 −0.5984 0.7376−0.4992 0.7597 −0.5474 0.7595 −0.5496 0.7139 −0.4523 0.7367 −0.50040.7365 −0.5008 0.6902 −0.4054 0.7130 −0.4518 0.7128 −0.4504 0.6664−0.3585 0.6892 −0.4032 0.6890 −0.4000 0.6427 −0.3115 0.6654 −0.35450.6651 −0.3496 0.6189 −0.2646 0.6416 −0.3059 0.6411 −0.2993 0.5951−0.2177 0.6178 −0.2573 0.6171 −0.2489 0.5713 −0.1708 0.5939 −0.20870.5930 −0.1986 0.5475 −0.1239 0.5700 −0.1600 0.5688 −0.1483 0.5235−0.0770 0.5461 −0.1114 0.5446 −0.0981 0.4993 −0.0303 0.5221 −0.06290.5201 −0.0479 0.4748 0.0162 0.4978 −0.0144 0.4955 0.0022 0.4497 0.06250.4732 0.0339 0.4705 0.0522 0.4238 0.1083 0.4481 0.0820 0.4450 0.10190.3970 0.1536 0.4223 0.1296 0.4189 0.1513 0.3699 0.1967 0.3955 0.17680.3920 0.2003 0.3411 0.2387 0.3686 0.2218 0.3650 0.2470 0.3114 0.27780.3401 0.2658 0.3366 0.2930 0.2815 0.3122 0.3108 0.3071 0.3076 0.33640.2499 0.3427 0.2813 0.3437 0.2786 0.3751 0.2177 0.3669 0.2503 0.37640.2483 0.4104 0.1852 0.3844 0.2186 0.4032 0.2176 0.4400 0.1532 0.39360.1866 0.4233 0.1864 0.4631 0.1235 0.3968 0.1548 0.4355 0.1551 0.47890.0974 0.3996 0.1247 0.4409 0.1248 0.4873 0.0752 0.4049 0.0977 0.44450.0972 0.4922 0.0571 0.4116 0.0749 0.4501 0.0736 0.4982 0.0432 0.41900.0563 0.4572 0.0546 0.5058 0.0331 0.4260 0.0419 0.4649 0.0400 0.51410.0265 0.4318 0.0316 0.4723 0.0295 0.5219 0.0216 0.4368 0.0249 0.47830.0227 0.5283 0.0182 0.4408 0.0200 0.4836 0.0178 0.5339 0.0161 0.44360.0166 0.4879 0.0144 0.5384 0.0141 0.4465 0.0145 0.4908 0.0124 0.54160.0132 0.4480 0.0125 0.4939 0.0105 0.5448 0.0122 0.4495 0.0116 0.49540.0096 0.5464 0.0111 0.4516 0.0107 0.4970 0.0087 0.5481 0.0100 0.45360.0096 0.4991 0.0076 0.5503 0.0079 0.4579 0.0085 0.5013 0.0067 0.55250.0061 0.4623 0.0066 0.5057 0.0049 0.5570 0.0038 0.4690 0.0049 0.51020.0034 0.5617 0.0016 0.4782 0.0028 0.5171 0.0017 0.5688 0.0001 0.48990.0010 0.5265 0.0003 0.5784 0.0000 0.5065 0.0000 0.5384 0.0000 0.5906Section S12 Section S13 Section S14 X/B_(X) Y/B_(X) X/B_(X) Y/B_(X)X/B_(X) Y/B_(X) 0.0000 0.6351 0.0000 0.6880 0.0000 0.7510 0.0005 0.64740.0001 0.6979 0.0001 0.7584 0.0034 0.6644 0.0017 0.7102 0.0012 0.76830.0102 0.6855 0.0061 0.7269 0.0042 0.7803 0.0219 0.7099 0.0148 0.74740.0105 0.7964 0.0390 0.7370 0.0287 0.7708 0.0214 0.8158 0.0620 0.76600.0482 0.7963 0.0379 0.8375 0.0924 0.7952 0.0740 0.8230 0.0602 0.86050.1319 0.8205 0.1074 0.8483 0.0889 0.8834 0.1808 0.8362 0.1499 0.86810.1252 0.9031 0.2366 0.8372 0.2010 0.8763 0.1698 0.9154 0.2952 0.82170.2572 0.8686 0.2216 0.9149 0.3511 0.7924 0.3142 0.8450 0.2768 0.89850.4052 0.7508 0.3676 0.8095 0.3314 0.8674 0.4551 0.7008 0.4189 0.76330.3819 0.8262 0.4997 0.6460 0.4662 0.7097 0.4306 0.7758 0.5413 0.58580.5087 0.6522 0.4756 0.7190 0.5791 0.5232 0.5484 0.5897 0.5162 0.65890.6137 0.4588 0.5847 0.5253 0.5542 0.5943 0.6457 0.3929 0.6183 0.45930.5892 0.5280 0.6753 0.3260 0.6495 0.3922 0.6217 0.4605 0.7029 0.25820.6786 0.3242 0.6521 0.3920 0.7287 0.1898 0.7059 0.2554 0.6806 0.32270.7529 0.1207 0.7315 0.1860 0.7073 0.2527 0.7756 0.0512 0.7557 0.11600.7326 0.1822 0.7971 −0.0188 0.7784 0.0456 0.7564 0.1112 0.8173 −0.08910.7999 −0.0252 0.7789 0.0397 0.8363 −0.1597 0.8201 −0.0964 0.8002−0.0321 0.8544 −0.2306 0.8392 −0.1679 0.8203 −0.1043 0.8713 −0.30180.8572 −0.2397 0.8393 −0.1768 0.8868 −0.3708 0.8742 −0.3117 0.8572−0.2495 0.9015 −0.4399 0.8896 −0.3815 0.8741 −0.3225 0.9148 −0.50690.9041 −0.4515 0.8894 −0.3933 0.9266 −0.5691 0.9172 −0.5193 0.9039−0.4643 0.9389 −0.6288 0.9288 −0.5824 0.9169 −0.5330 0.9509 −0.68360.9409 −0.6429 0.9285 −0.5969 0.9621 −0.7335 0.9526 −0.6983 0.9406−0.6581 0.9716 −0.7789 0.9636 −0.7490 0.9523 −0.7143 0.9796 −0.81950.9728 −0.7949 0.9634 −0.7656 0.9865 −0.8554 0.9806 −0.8361 0.9727−0.8121 0.9923 −0.8866 0.9872 −0.8725 0.9805 −0.8539 0.9969 −0.91300.9928 −0.9040 0.9871 −0.8907 1.0000 −0.9347 0.9971 −0.9308 0.9927−0.9227 1.0000 −0.9518 1.0000 −0.9528 0.9971 −0.9498 0.9963 −0.96330.9998 −0.9701 1.0000 −0.9721 0.9908 −0.9714 0.9959 −0.9818 0.9996−0.9896 0.9856 −0.9765 0.9903 −0.9899 0.9955 −1.0014 0.9816 −0.97930.9850 −0.9950 0.9898 −1.0095 0.9773 −0.9817 0.9810 −0.9978 0.9844−1.0147 0.9751 −0.9826 0.9766 −1.0002 0.9803 −1.0176 0.9728 −0.98350.9744 −1.0012 0.9759 −1.0199 0.9710 −0.9840 0.9720 −1.0020 0.9736−1.0209 0.9691 −0.9844 0.9701 −1.0025 0.9712 −1.0218 0.9653 −0.98490.9682 −1.0029 0.9693 −1.0223 0.9615 −0.9851 0.9643 −1.0035 0.9672−1.0227 0.9557 −0.9846 0.9603 −1.0037 0.9632 −1.0233 0.9483 −0.98280.9544 −1.0032 0.9591 −1.0234 0.9397 −0.9786 0.9467 −1.0012 0.9529−1.0229 0.9301 −0.9693 0.9379 −0.9968 0.9450 −1.0208 0.9222 −0.95390.9281 −0.9870 0.9359 −1.0161 0.9148 −0.9342 0.9201 −0.9711 0.9259−1.0058 0.9057 −0.9110 0.9127 −0.9506 0.9178 −0.9892 0.8955 −0.88420.9035 −0.9266 0.9101 −0.9680 0.8838 −0.8538 0.8932 −0.8987 0.9006−0.9430 0.8708 −0.8198 0.8815 −0.8672 0.8899 −0.9141 0.8567 −0.78220.8683 −0.8319 0.8778 −0.8814 0.8413 −0.7409 0.8541 −0.7928 0.8642−0.8449 0.8233 −0.6965 0.8386 −0.7500 0.8495 −0.8043 0.8035 −0.65090.8204 −0.7040 0.8334 −0.7599 0.7814 −0.6020 0.8004 −0.6565 0.8147−0.7121 0.7585 −0.5514 0.7781 −0.6058 0.7940 −0.6629 0.7355 −0.50080.7549 −0.5532 0.7710 −0.6102 0.7117 −0.4485 0.7316 −0.5007 0.7472−0.5556 0.6877 −0.3962 0.7075 −0.4464 0.7234 −0.5009 0.6637 −0.34400.6833 −0.3921 0.6987 −0.4444 0.6395 −0.2918 0.6589 −0.3378 0.6740−0.3880 0.6152 −0.2396 0.6345 −0.2837 0.6492 −0.3315 0.5908 −0.18750.6099 −0.2295 0.6244 −0.2751 0.5662 −0.1355 0.5851 −0.1754 0.5995−0.2187 0.5415 −0.0835 0.5602 −0.1214 0.5745 −0.1623 0.5165 −0.03160.5351 −0.0675 0.5494 −0.1060 0.4913 0.0202 0.5097 −0.0137 0.5241−0.0497 0.4658 0.0718 0.4841 0.0400 0.4986 0.0064 0.4399 0.1232 0.45820.0936 0.4729 0.0625 0.4134 0.1744 0.4319 0.1470 0.4469 0.1184 0.38620.2252 0.4051 0.2001 0.4205 0.1741 0.3590 0.2738 0.3777 0.2530 0.39380.2297 0.3308 0.3218 0.3505 0.3037 0.3665 0.2850 0.3021 0.3673 0.32240.3539 0.3396 0.3382 0.2737 0.4084 0.2941 0.4017 0.3118 0.3909 0.24430.4462 0.2663 0.4452 0.2840 0.4414 0.2146 0.4788 0.2378 0.4858 0.25690.4875 0.1845 0.5053 0.2093 0.5215 0.2293 0.5310 0.1541 0.5251 0.18040.5515 0.2018 0.5697 0.1238 0.5369 0.1510 0.5752 0.1740 0.6031 0.09570.5436 0.1211 0.5907 0.1457 0.6306 0.0716 0.5503 0.0928 0.5999 0.11670.6500 0.0521 0.5588 0.0683 0.6079 0.0886 0.6622 0.0373 0.5677 0.04870.6174 0.0640 0.6721 0.0268 0.5761 0.0338 0.6272 0.0444 0.6831 0.02000.5830 0.0233 0.6364 0.0296 0.6941 0.0152 0.5890 0.0167 0.6438 0.01950.7042 0.0119 0.5938 0.0121 0.6502 0.0131 0.7123 0.0100 0.5971 0.00900.6553 0.0088 0.7192 0.0082 0.6005 0.0072 0.6589 0.0061 0.7247 0.00730.6022 0.0056 0.6625 0.0045 0.7285 0.0065 0.6040 0.0049 0.6644 0.00320.7324 0.0056 0.6063 0.0042 0.6662 0.0026 0.7343 0.0047 0.6086 0.00340.6686 0.0021 0.7363 0.0032 0.6132 0.0027 0.6709 0.0015 0.7387 0.00200.6180 0.0015 0.6757 0.0010 0.7411 0.0007 0.6253 0.0007 0.6806 0.00040.7461 0.0000 0.6351 0.0000 0.6880 0.0000 0.7510 Section S15 Section S16Section S17 X/B_(X) Y/B_(X) X/B_(X) Y/B_(X) X/B_(X) Y/B_(X) 0.00000.8250 0.0000 0.9029 0.0000 0.9910 0.0003 0.8299 0.0001 0.9054 0.00020.9957 0.0013 0.8373 0.0002 0.9079 0.0004 0.9981 0.0038 0.8469 0.00090.9130 0.0007 1.0004 0.0084 0.8584 0.0019 0.9179 0.0012 1.0030 0.01690.8736 0.0042 0.9251 0.0018 1.0055 0.0305 0.8912 0.0082 0.9343 0.00341.0105 0.0499 0.9104 0.0148 0.9451 0.0054 1.0154 0.0753 0.9299 0.02600.9587 0.0090 1.0224 0.1073 0.9474 0.0426 0.9740 0.0150 1.0309 0.14630.9595 0.0653 0.9898 0.0239 1.0406 0.1919 0.9622 0.0943 1.0045 0.03811.0522 0.2427 0.9519 0.1297 1.0150 0.0583 1.0643 0.2953 0.9268 0.17101.0172 0.0847 1.0758 0.3466 0.8887 0.2165 1.0083 0.1175 1.0846 0.39420.8426 0.2645 0.9868 0.1567 1.0863 0.4402 0.7884 0.3128 0.9530 0.20001.0762 0.4832 0.7286 0.3600 0.9087 0.2441 1.0532 0.5221 0.6662 0.40430.8583 0.2873 1.0193 0.5588 0.5996 0.4479 0.8007 0.3296 0.9768 0.59260.5315 0.4890 0.7384 0.3717 0.9271 0.6240 0.4624 0.5265 0.6739 0.41240.8730 0.6534 0.3924 0.5620 0.6055 0.4535 0.8126 0.6811 0.3217 0.59480.5357 0.4930 0.7482 0.7071 0.2503 0.6252 0.4649 0.5294 0.6819 0.73170.1785 0.6536 0.3933 0.5641 0.6118 0.7549 0.1062 0.6802 0.3210 0.59590.5404 0.7769 0.0335 0.7052 0.2481 0.6253 0.4679 0.7977 −0.0395 0.72870.1748 0.6525 0.3946 0.8174 −0.1128 0.7510 0.1010 0.6778 0.3205 0.8361−0.1865 0.7722 0.0270 0.7015 0.2460 0.8538 −0.2603 0.7923 −0.0474 0.72370.1710 0.8705 −0.3344 0.8114 −0.1220 0.7447 0.0957 0.8858 −0.4062 0.8295−0.1969 0.7647 0.0200 0.9003 −0.4782 0.8469 −0.2720 0.7837 −0.05580.9135 −0.5478 0.8634 −0.3472 0.8019 −0.1319 0.9252 −0.6126 0.8787−0.4201 0.8194 −0.2081 0.9376 −0.6747 0.8933 −0.4932 0.8362 −0.28450.9497 −0.7316 0.9067 −0.5638 0.8524 −0.3610 0.9612 −0.7835 0.9188−0.6295 0.8676 −0.4351 0.9709 −0.8306 0.9318 −0.6924 0.8825 −0.50920.9791 −0.8729 0.9446 −0.7500 0.8963 −0.5809 0.9861 −0.9102 0.9569−0.8025 0.9091 −0.6474 0.9921 −0.9425 0.9673 −0.8502 0.9230 −0.71110.9968 −0.9700 0.9764 −0.8929 0.9369 −0.7694 1.0000 −0.9925 0.9842−0.9306 0.9503 −0.8225 0.9994 −1.0102 0.9909 −0.9633 0.9620 −0.87060.9952 −1.0221 0.9962 −0.9910 0.9722 −0.9137 0.9893 −1.0304 1.0000−1.0138 0.9812 −0.9518 0.9838 −1.0355 0.9993 −1.0318 0.9891 −0.98480.9796 −1.0384 0.9948 −1.0438 0.9953 −1.0127 0.9751 −1.0408 0.9888−1.0521 1.0000 −1.0358 0.9728 −1.0418 0.9831 −1.0573 0.9992 −1.05400.9704 −1.0427 0.9789 −1.0602 0.9945 −1.0661 0.9684 −1.0432 0.9744−1.0626 0.9883 −1.0745 0.9663 −1.0436 0.9720 −1.0636 0.9826 −1.07970.9620 −1.0442 0.9696 −1.0645 0.9782 −1.0827 0.9578 −1.0444 0.9674−1.0650 0.9736 −1.0851 0.9514 −1.0438 0.9653 −1.0655 0.9712 −1.08610.9432 −1.0415 0.9608 −1.0661 0.9688 −1.0870 0.9337 −1.0364 0.9564−1.0662 0.9665 −1.0876 0.9236 −1.0256 0.9497 −1.0655 0.9642 −1.08800.9153 −1.0082 0.9412 −1.0631 0.9596 −1.0886 0.9069 −0.9863 0.9315−1.0576 0.9550 −1.0887 0.8969 −0.9604 0.9211 −1.0461 0.9480 −1.08790.8855 −0.9305 0.9125 −1.0279 0.9391 −1.0852 0.8726 −0.8966 0.9033−1.0053 0.9290 −1.0794 0.8582 −0.8587 0.8924 −0.9785 0.9185 −1.06710.8425 −0.8167 0.8800 −0.9475 0.9096 −1.0480 0.8255 −0.7706 0.8659−0.9124 0.8992 −1.0247 0.8057 −0.7210 0.8501 −0.8731 0.8871 −0.99700.7839 −0.6699 0.8331 −0.8296 0.8732 −0.9649 0.7599 −0.6151 0.8146−0.7818 0.8575 −0.9286 0.7350 −0.5584 0.7932 −0.7304 0.8400 −0.88800.7102 −0.5016 0.7699 −0.6774 0.8211 −0.8429 0.6847 −0.4427 0.7443−0.6205 0.8006 −0.7935 0.6593 −0.3838 0.7180 −0.5615 0.7771 −0.74020.6340 −0.3249 0.6919 −0.5024 0.7518 −0.6852 0.6087 −0.2660 0.6652−0.4410 0.7240 −0.6262 0.5835 −0.2070 0.6388 −0.3796 0.6958 −0.56490.5584 −0.1480 0.6128 −0.3180 0.6680 −0.5033 0.5333 −0.0890 0.5870−0.2562 0.6398 −0.4393 0.5081 −0.0300 0.5616 −0.1944 0.6123 −0.37510.4828 0.0289 0.5364 −0.1324 0.5853 −0.3105 0.4573 0.0878 0.5115 −0.07030.5590 −0.2457 0.4316 0.1465 0.4868 −0.0081 0.5333 −0.1807 0.4057 0.20510.4620 0.0540 0.5083 −0.1153 0.3793 0.2636 0.4373 0.1161 0.4839 −0.04970.3526 0.3218 0.4123 0.1782 0.4599 0.0160 0.3261 0.3779 0.3872 0.24010.4361 0.0818 0.2989 0.4336 0.3617 0.3020 0.4125 0.1477 0.2718 0.48700.3358 0.3637 0.3888 0.2136 0.2454 0.5360 0.3102 0.4231 0.3650 0.27950.2186 0.5825 0.2839 0.4822 0.3408 0.3453 0.1921 0.6242 0.2576 0.53890.3163 0.4109 0.1654 0.6608 0.2320 0.5910 0.2919 0.4741 0.1383 0.69180.2060 0.6405 0.2667 0.5370 0.1104 0.7152 0.1803 0.6852 0.2414 0.59740.0831 0.7311 0.1546 0.7248 0.2166 0.6529 0.0589 0.7436 0.1288 0.75900.1914 0.7055 0.0394 0.7565 0.1026 0.7865 0.1664 0.7531 0.0251 0.76910.0767 0.8069 0.1417 0.7956 0.0154 0.7803 0.0530 0.8229 0.1172 0.83260.0095 0.7892 0.0340 0.8381 0.0932 0.8643 0.0057 0.7967 0.0203 0.85260.0693 0.8899 0.0034 0.8027 0.0113 0.8652 0.0467 0.9103 0.0022 0.80670.0062 0.8750 0.0285 0.9284 0.0012 0.8108 0.0030 0.8833 0.0157 0.94510.0009 0.8129 0.0013 0.8897 0.0076 0.9594 0.0006 0.8150 0.0006 0.89410.0034 0.9703 0.0003 0.8175 0.0001 0.8985 0.0011 0.9794 0.0001 0.82000.0000 0.9007 0.0002 0.9864 0.0000 0.8250 0.0000 0.9029 0.0000 0.9910

TABLE 5 Normalized Platform (ID) and Shroud (OD) Coordinates (Vanes)Tolerance: ±0.05″ (±1.27 mm) X_(ID)/ SD_(ID) X_(OD)/ S_(OD) B_(Xroot) (Y= 0) B_(Xroot) (Y = 0) −0.2859 −0.1706 −0.1514 1.2259 −0.2613 −0.1492−0.1236 1.2073 −0.2318 −0.1313 −0.0912 1.1931 −0.1973 −0.1187 −0.05491.1849 −0.1597 −0.1119 −0.0169 1.1834 −0.1218 −0.1057 0.0213 1.1827−0.0840 −0.0995 0.0593 1.1805 −0.0461 −0.0932 0.0972 1.1771 −0.0082−0.0870 0.1349 1.1729 0.0296 −0.0808 0.1726 1.1683 0.0675 −0.0746 0.21021.1636 0.1053 −0.0683 0.2477 1.1588 0.1432 −0.0621 0.2853 1.1541 0.1811−0.0559 0.3230 1.1495 0.2190 −0.0497 0.3606 1.1449 0.2568 −0.0434 0.39821.1402 0.2946 −0.0371 0.4358 1.1356 0.3325 −0.0309 0.4734 1.1309 0.3705−0.0252 0.5110 1.1263 0.4087 −0.0202 0.5487 1.1216 0.4472 −0.0162 0.58631.1170 0.4858 −0.0131 0.6239 1.1124 0.5246 −0.0112 0.6615 1.1077 0.5634−0.0102 0.6991 1.1030 0.6023 −0.0098 0.7367 1.0983 0.6411 −0.0098 0.77441.0937 0.6800 −0.0100 0.8120 1.0892 0.7188 −0.0101 0.8496 1.0846 0.7577−0.0101 0.8872 1.0799 0.7966 −0.0101 0.9248 1.0749 0.8354 −0.0101 0.96241.0704 0.8743 −0.0101 1.0003 1.0673 0.9131 −0.0101 1.0384 1.0659 0.9520−0.0100 1.0766 1.0660 0.9909 −0.0100 1.1148 1.0668 1.0297 −0.0099 1.15291.0681 1.0686 −0.0096 1.1910 1.0696 1.1074 −0.0092 1.2292 1.0712 1.1463−0.0088 1.2673 1.0729 1.1851 −0.0088 1.3053 1.0748

TABLE 6 Normalized Platform (ID) Coordinates (Blades) Tolerance: ±0.05″(±1.27 mm) X_(P)/B_(Xroot) Y_(P)/τ_(root) S_(P) −0.4202 −0.3680 −0.0257−0.4200 −0.3470 −0.0253 −0.4198 −0.3259 −0.0250 −0.4196 −0.3048 −0.0247−0.4193 −0.2837 −0.0245 −0.4191 −0.2626 −0.0243 −0.4189 −0.2415 −0.0241−0.4187 −0.2204 −0.0240 −0.4184 −0.1993 −0.0239 −0.4182 −0.1782 −0.0239−0.4180 −0.1572 −0.0239 −0.4178 −0.1361 −0.0239 −0.4176 −0.1150 −0.0240−0.4173 −0.0939 −0.0241 −0.4171 −0.0728 −0.0243 −0.4169 −0.0517 −0.0245−0.4167 −0.0306 −0.0247 −0.4164 −0.0095 −0.0250 −0.4162 0.0116 −0.0253−0.4160 0.0326 −0.0257 −0.4158 0.0537 −0.0261 −0.4155 0.0748 −0.0265−0.4153 0.0959 −0.0270 −0.4151 0.1170 −0.0275 −0.4149 0.1380 −0.0281−0.4146 0.1591 −0.0287 −0.4144 0.1802 −0.0293 −0.4142 0.2012 −0.0300−0.4140 0.2223 −0.0307 −0.4137 0.2434 −0.0315 −0.4135 0.2644 −0.0323−0.4133 0.2855 −0.0331 −0.4131 0.3065 −0.0340 −0.4128 0.3275 −0.0349−0.4126 0.3486 −0.0359 −0.4124 0.3696 −0.0369 −0.4122 0.3906 −0.0379−0.4120 0.4116 −0.0390 −0.4117 0.4327 −0.0401 −0.4115 0.4537 −0.0413−0.4113 0.4747 −0.0425 −0.4111 0.4957 −0.0437 −0.4108 0.5166 −0.0450−0.4106 0.5376 −0.0463 −0.4104 0.5586 −0.0476 −0.3939 −0.3893 −0.0261−0.3937 −0.3682 −0.0257 −0.3935 −0.3471 −0.0253 −0.3933 −0.3260 −0.0250−0.3931 −0.3050 −0.0247 −0.3928 −0.2839 −0.0245 −0.3926 −0.2628 −0.0243−0.3924 −0.2417 −0.0241 −0.3922 −0.2206 −0.0240 −0.3919 −0.1995 −0.0239−0.3917 −0.1784 −0.0239 −0.3915 −0.1573 −0.0239 −0.3913 −0.1362 −0.0239−0.3910 −0.1151 −0.0240 −0.3908 −0.0940 −0.0241 −0.3906 −0.0730 −0.0243−0.3904 −0.0519 −0.0245 −0.3901 −0.0308 −0.0247 −0.3899 −0.0097 −0.0250−0.3897 0.0114 −0.0253 −0.3895 0.0325 −0.0257 −0.3892 0.0536 −0.0261−0.3890 0.0746 −0.0265 −0.3888 0.0957 −0.0270 −0.3886 0.1168 −0.0275−0.3883 0.1379 −0.0281 −0.3881 0.1589 −0.0287 −0.3879 0.1800 −0.0293−0.3877 0.2011 −0.0300 −0.3874 0.2221 −0.0307 −0.3872 0.2432 −0.0315−0.3870 0.2642 −0.0323 −0.3868 0.2853 −0.0331 −0.3866 0.3063 −0.0340−0.3863 0.3274 −0.0349 −0.3861 0.3484 −0.0359 −0.3859 0.3694 −0.0369−0.3857 0.3905 −0.0379 −0.3854 0.4115 −0.0390 −0.3852 0.4325 −0.0401−0.3850 0.4535 −0.0413 −0.3848 0.4745 −0.0425 −0.3845 0.4955 −0.0437−0.3843 0.5165 −0.0450 −0.3841 0.5375 −0.0463 −0.3839 0.5584 −0.0476−0.3674 −0.3895 −0.0261 −0.3672 −0.3684 −0.0257 −0.3670 −0.3473 −0.0253−0.3668 −0.3262 −0.0250 −0.3665 −0.3051 −0.0247 −0.3663 −0.2840 −0.0245−0.3661 −0.2629 −0.0243 −0.3659 −0.2419 −0.0241 −0.3656 −0.2208 −0.0240−0.3654 −0.1997 −0.0239 −0.3652 −0.1786 −0.0239 −0.3650 −0.1575 −0.0239−0.3647 −0.1364 −0.0239 −0.3645 −0.1153 −0.0240 −0.3643 −0.0942 −0.0241−0.3641 −0.0731 −0.0243 −0.3638 −0.0520 −0.0245 −0.3636 −0.0309 −0.0247−0.3634 −0.0099 −0.0250 −0.3632 0.0112 −0.0253 −0.3629 0.0323 −0.0257−0.3627 0.0534 −0.0261 −0.3625 0.0745 −0.0265 −0.3623 0.0956 −0.0270−0.3621 0.1166 −0.0275 −0.3618 0.1377 −0.0281 −0.3616 0.1588 −0.0287−0.3614 0.1798 −0.0293 −0.3612 0.2009 −0.0300 −0.3609 0.2220 −0.0307−0.3607 0.2430 −0.0315 −0.3605 0.2641 −0.0323 −0.3603 0.2851 −0.0331−0.3600 0.3062 −0.0340 −0.3598 0.3272 −0.0349 −0.3596 0.3482 −0.0359−0.3594 0.3693 −0.0369 −0.3591 0.3903 −0.0379 −0.3589 0.4113 −0.0390−0.3587 0.4323 −0.0401 −0.3585 0.4533 −0.0413 −0.3582 0.4743 −0.0425−0.3580 0.4953 −0.0437 −0.3578 0.5163 −0.0450 −0.3576 0.5373 −0.0463−0.3409 −0.3896 −0.0261 −0.3407 −0.3685 −0.0257 −0.3405 −0.3475 −0.0253−0.3402 −0.3264 −0.0250 −0.3400 −0.3053 −0.0247 −0.3398 −0.2842 −0.0245−0.3396 −0.2631 −0.0243 −0.3393 −0.2420 −0.0241 −0.3391 −0.2209 −0.0240−0.3389 −0.1998 −0.0239 −0.3387 −0.1787 −0.0239 −0.3384 −0.1577 −0.0239−0.3382 −0.1366 −0.0239 −0.3380 −0.1155 −0.0240 −0.3378 −0.0944 −0.0241−0.3375 −0.0733 −0.0243 −0.3373 −0.0522 −0.0245 −0.3371 −0.0311 −0.0247−0.3369 −0.0100 −0.0250 −0.3367 0.0111 −0.0253 −0.3364 0.0321 −0.0257−0.3362 0.0532 −0.0261 −0.3360 0.0743 −0.0265 −0.3358 0.0954 −0.0270−0.3355 0.1165 −0.0275 −0.3353 0.1375 −0.0281 −0.3351 0.1586 −0.0287−0.3349 0.1797 −0.0293 −0.3346 0.2007 −0.0300 −0.3344 0.2218 −0.0307−0.3342 0.2428 −0.0315 −0.3340 0.2639 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0.03970.0884 −0.4278 0.0384 0.0885 −0.3698 0.0401 0.0885 −0.4470 0.0375 0.0887−0.4661 0.0366 0.0888 −0.3503 0.0403 0.0890 −0.4851 0.0356 0.0892−0.3306 0.0404 0.0892 −0.5042 0.0345 0.0895 −0.5232 0.0334 0.0898−0.5422 0.0323 0.0898 −0.3109 0.0402 0.0906 −0.2910 0.0398 0.0916−0.2710 0.0391 0.0928 −0.2509 0.0382 0.0940 −0.2308 0.0372 0.0954−0.2107 0.0360 0.0968 −0.1906 0.0347 0.0981 −0.1706 0.0334 0.0995−0.1506 0.0322 0.1007 −0.1306 0.0309 0.1008 0.4092 0.0225 0.1009 0.39020.0230 0.1010 −0.3847 0.0481 0.1010 −0.4040 0.0475 0.1011 0.3712 0.02350.1011 −0.3652 0.0486 0.1011 −0.4233 0.0467 0.1013 0.3521 0.0240 0.1014−0.4425 0.0458 0.1014 −0.3457 0.0488 0.1014 0.3331 0.0244 0.1016 0.31400.0249 0.1017 −0.4616 0.0448 0.1017 0.2949 0.0253 0.1019 −0.3260 0.04880.1019 0.2757 0.0257 0.1020 −0.4806 0.0437 0.1021 0.2565 0.0260 0.10220.2373 0.0263 0.1024 −0.4996 0.0425 0.1024 0.2180 0.0265 0.1026 −0.30610.0485 0.1026 0.1987 0.0267 0.1027 −0.5186 0.0412 0.1031 −0.5376 0.04000.1035 −0.2861 0.0480 0.1046 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0.1274−0.4337 0.0616 0.1277 −0.4529 0.0605 0.1279 −0.2971 0.0649 0.1279 0.40250.0371 0.1281 −0.4720 0.0593 0.1283 0.3834 0.0375 0.1286 −0.4911 0.05810.1286 0.3643 0.0378 0.1287 −0.2771 0.0645 0.1289 0.3452 0.0381 0.1290−0.5101 0.0568 0.1293 0.3261 0.0383 0.1294 −0.5292 0.0555 0.1296 0.30700.0385 0.1298 −0.5482 0.0543 0.1298 −0.2570 0.0637 0.1300 0.2878 0.03860.1305 0.2686 0.0386 0.1310 0.2493 0.0385 0.1310 −0.2368 0.0627 0.13150.2301 0.0384 0.1322 0.2108 0.0381 0.1324 −0.2166 0.0615 0.1338 −0.19640.0601 0.1353 −0.1762 0.0587 0.1368 −0.1561 0.0572 0.1399 −0.3519 0.07220.1399 −0.3714 0.0716 0.1400 −0.3323 0.0726 0.1400 −0.3908 0.0708 0.1402−0.3126 0.0728 0.1403 −0.4101 0.0700 0.1406 −0.4294 0.0690 0.1407−0.2927 0.0728 0.1409 −0.4486 0.0679 0.1410 0.4082 0.0444 0.1413 −0.27280.0725 0.1413 −0.4677 0.0667 0.1414 0.3891 0.0448 0.1417 −0.4868 0.06550.1417 0.3700 0.0451 0.1421 −0.5060 0.0643 0.1421 0.3508 0.0453 0.1421−0.2527 0.0720 0.1425 −0.5251 0.0631 0.1425 0.3317 0.0454 0.1428 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0.08590.1673 −0.2627 0.0876 0.1673 −0.3611 0.0852 0.1674 0.4010 0.0590 0.1675−0.3805 0.0844 0.1676 −0.2428 0.0877 0.1678 −0.3999 0.0835 0.1678 0.38180.0593 0.1679 −0.2229 0.0876 0.1680 −0.4192 0.0826 0.1683 0.3627 0.05950.1683 −0.4384 0.0816 0.1684 −0.2029 0.0875 0.1686 −0.4577 0.0805 0.1689−0.1829 0.0872 0.1689 0.3436 0.0594 0.1689 −0.4769 0.0795 0.1692 −0.49610.0784 0.1694 −0.1629 0.0868 0.1694 −0.5153 0.0773 0.1696 −0.5345 0.07630.1696 0.3245 0.0592 0.1698 −0.5537 0.0752 0.1699 −0.1430 0.0864 0.1701−0.5729 0.0740 0.1705 0.3054 0.0587 0.1717 0.2863 0.0580 0.1730 0.26730.0570 0.1746 0.2483 0.0556 0.1812 −0.2374 0.0949 0.1812 −0.2572 0.09450.1812 −0.2176 0.0952 0.1813 −0.2770 0.0941 0.1813 −0.1977 0.0955 0.18140.3883 0.0660 0.1814 −0.2967 0.0935 0.1814 −0.1779 0.0956 0.1816 −0.15800.0957 0.1816 −0.3164 0.0929 0.1817 −0.1381 0.0957 0.1817 −0.3360 0.09210.1819 0.3691 0.0661 0.1820 −0.3555 0.0914 0.1822 −0.3749 0.0905 0.1824−0.3943 0.0897 0.1826 0.3500 0.0660 0.1827 −0.4137 0.0888 0.1829 −0.43300.0878 0.1831 −0.4523 0.0869 0.1834 −0.4716 0.0859 0.1834 0.3309 0.06570.1836 −0.4909 0.0849 0.1837 −0.5102 0.0839 0.1839 −0.5295 0.0829 0.1840−0.5487 0.0819 0.1842 −0.5679 0.0808 0.1845 0.3118 0.0650 0.1858 0.29270.0640 0.1875 0.2737 0.0627 0.1895 0.2547 0.0609 0.1950 −0.1528 0.10370.1952 −0.1726 0.1032 0.1954 −0.1924 0.1027 0.1956 0.3947 0.0723 0.1957−0.2122 0.1021 0.1959 −0.2319 0.1015 0.1961 0.3755 0.0724 0.1962 −0.25170.1008 0.1965 −0.2714 0.1001 0.1967 −0.2911 0.0994 0.1969 0.3563 0.07220.1970 −0.3108 0.0987 0.1973 −0.3304 0.0979 0.1975 −0.3499 0.0971 0.1977−0.3694 0.0962 0.1979 0.3372 0.0717 0.1980 −0.3888 0.0954 0.1982 −0.40820.0945 0.1984 −0.4276 0.0936 0.1986 −0.4469 0.0927 0.1987 −0.4663 0.09180.1989 −0.4856 0.0909 0.1990 −0.5050 0.0900 0.1991 0.3180 0.0709 0.1991−0.5243 0.0890 0.1993 −0.5436 0.0880 0.1995 −0.5629 0.0869 0.1997−0.5820 0.0857 0.2007 0.2990 0.0696 0.2026 0.2799 0.0680 0.2049 0.26100.0658 0.2101 −0.1473 0.1106 0.2105 −0.1671 0.1098 0.2110 −0.1868 0.10900.2115 0.3818 0.0779 0.2115 −0.2065 0.1082 0.2120 −0.2262 0.1073 0.21230.3626 0.0776 0.2124 −0.2459 0.1064 0.2128 −0.2657 0.1056 0.2132 −0.28540.1047 0.2134 0.3435 0.0770 0.2135 −0.3050 0.1039 0.2138 −0.3246 0.10300.2141 −0.3441 0.1022 0.2143 −0.3636 0.1014 0.2146 −0.3831 0.1006 0.2148−0.4026 0.0997 0.2148 0.3243 0.0760 0.2149 −0.4220 0.0989 0.2151 −0.44140.0981 0.2152 −0.4608 0.0972 0.2153 −0.4802 0.0963 0.2154 −0.4995 0.09540.2155 −0.5189 0.0945 0.2157 −0.5382 0.0935 0.2159 −0.5575 0.0924 0.2162−0.5767 0.0911 0.2166 0.3052 0.0746 0.2187 0.2862 0.0727 0.2213 0.26730.0702 0.2274 −0.1611 0.1153 0.2280 −0.1808 0.1143 0.2287 −0.2005 0.11330.2290 0.3691 0.0823 0.2293 −0.2202 0.1123 0.2299 −0.2399 0.1113 0.23020.3499 0.0816 0.2304 −0.2596 0.1103 0.2308 −0.2793 0.1094 0.2312 −0.29900.1085 0.2315 −0.3186 0.1077 0.2317 0.3308 0.0804 0.2318 −0.3382 0.10680.2320 −0.3577 0.1060 0.2322 −0.3772 0.1052 0.2324 −0.3967 0.1044 0.2325−0.4161 0.1036 0.2326 −0.4356 0.1028 0.2328 −0.4550 0.1019 0.2329−0.4744 0.1011 0.2330 −0.4938 0.1002 0.2331 −0.5132 0.0992 0.2333−0.5325 0.0982 0.2336 −0.5518 0.0970 0.2336 0.3117 0.0788 0.2339 −0.57100.0957 0.2345 −0.5901 0.0941 0.2360 0.2927 0.0767 0.2459 −0.1548 0.11970.2466 −0.1745 0.1186 0.2470 0.3757 0.0861 0.2473 −0.1943 0.1175 0.2480−0.2140 0.1164 0.2482 0.3565 0.0852 0.2486 −0.2337 0.1154 0.2491 −0.25350.1144 0.2496 −0.2732 0.1134 0.2499 0.3373 0.0840 0.2500 −0.2929 0.11250.2503 −0.3125 0.1117 0.2505 −0.3322 0.1109 0.2508 −0.3517 0.1101 0.2509−0.3713 0.1093 0.2511 −0.3908 0.1085 0.2512 −0.4103 0.1077 0.2513−0.4298 0.1069 0.2515 −0.4492 0.1061 0.2516 −0.4687 0.1052 0.2517−0.4881 0.1043 0.2519 0.3182 0.0823 0.2519 −0.5075 0.1033 0.2521 −0.52680.1022 0.2524 −0.5461 0.1009 0.2529 −0.5653 0.0995 0.2535 −0.5844 0.09790.2543 0.2991 0.0800 0.2543 −0.6035 0.0960 0.2665 −0.1685 0.1221 0.2672−0.1883 0.1210 0.2675 0.3628 0.0882 0.2679 −0.2081 0.1198 0.2685 −0.22790.1188 0.2690 −0.2477 0.1178 0.2691 0.3436 0.0868 0.2694 −0.2675 0.11680.2698 −0.2872 0.1160 0.2701 −0.3069 0.1151 0.2703 −0.3266 0.1143 0.2705−0.3462 0.1136 0.2707 −0.3658 0.1128 0.2708 −0.3853 0.1120 0.2709−0.4048 0.1113 0.2711 −0.4244 0.1104 0.2711 0.3243 0.0851 0.2712 −0.44380.1096 0.2714 −0.4633 0.1087 0.2715 −0.4827 0.1077 0.2718 −0.5021 0.10660.2720 −0.5215 0.1054 0.2724 −0.5408 0.1041 0.2730 −0.5600 0.1026 0.27350.3051 0.0828 0.2736 −0.5792 0.1008 0.2745 −0.5983 0.0988 0.2877 0.36850.0904 0.2884 −0.1830 0.1236 0.2890 −0.2029 0.1225 0.2893 0.3491 0.08910.2895 −0.2228 0.1215 0.2900 −0.2426 0.1205 0.2904 −0.2625 0.1196 0.2907−0.2823 0.1188 0.2909 −0.3020 0.1180 0.2911 −0.3217 0.1172 0.2913−0.3414 0.1165 0.2913 0.3297 0.0873 0.2914 −0.3610 0.1157 0.2916 −0.38060.1150 0.2917 −0.4001 0.1142 0.2918 −0.4196 0.1133 0.2920 −0.4392 0.11240.2922 −0.4586 0.1115 0.2924 −0.4781 0.1104 0.2927 −0.4975 0.1093 0.2930−0.5169 0.1080 0.2935 −0.5362 0.1066 0.2936 0.3103 0.0850 0.2941 −0.55550.1049 0.2948 −0.5747 0.1031 0.2957 −0.5938 0.1010 0.2968 −0.6129 0.09860.3104 0.3537 0.0907 0.3105 −0.1787 0.1255 0.3110 −0.1987 0.1245 0.3115−0.2186 0.1236 0.3119 −0.2385 0.1227 0.3122 −0.2584 0.1218 0.3123 0.33410.0889 0.3124 −0.2783 0.1211 0.3126 −0.2981 0.1203 0.3128 −0.3178 0.11950.3130 −0.3375 0.1188 0.3131 −0.3572 0.1180 0.3132 −0.3768 0.1173 0.3134−0.3964 0.1164 0.3135 −0.4159 0.1155 0.3137 −0.4354 0.1146 0.3139−0.4550 0.1136 0.3142 −0.4744 0.1124 0.3145 0.3145 0.0867 0.3145 −0.49390.1112 0.3149 −0.5133 0.1098 0.3154 −0.5326 0.1083 0.3160 −0.5520 0.10660.3168 −0.5712 0.1046 0.3177 −0.5904 0.1025 0.3187 −0.6096 0.1001 0.3339−0.1957 0.1258 0.3339 0.3374 0.0902 0.3342 −0.2157 0.1250 0.3345 −0.23570.1242 0.3347 −0.2557 0.1235 0.3349 −0.2756 0.1227 0.3351 −0.2954 0.12200.3352 −0.3152 0.1213 0.3353 −0.3349 0.1205 0.3355 −0.3546 0.1197 0.3356−0.3742 0.1189 0.3358 −0.3938 0.1180 0.3359 0.3176 0.0881 0.3360 −0.41340.1171 0.3362 −0.4330 0.1161 0.3364 −0.4525 0.1149 0.3367 −0.4720 0.11370.3371 −0.4915 0.1124 0.3375 −0.5109 0.1109 0.3381 −0.5303 0.1093 0.3387−0.5497 0.1075 0.3394 −0.5690 0.1055 0.3403 −0.5883 0.1033 0.3413−0.6076 0.1009 0.3424 −0.6268 0.0982 0.3560 0.3393 0.0911 0.3575 −0.21430.1258 0.3577 −0.2343 0.1252 0.3577 0.3194 0.0892 0.3578 −0.2543 0.12450.3579 −0.2742 0.1238 0.3581 −0.2941 0.1231 0.3582 −0.3139 0.1224 0.3583−0.3337 0.1216 0.3585 −0.3534 0.1208 0.3586 −0.3730 0.1199 0.3588−0.3927 0.1189 0.3590 −0.4123 0.1179 0.3593 −0.4318 0.1168 0.3595−0.4514 0.1156 0.3599 −0.4709 0.1143 0.3602 −0.4905 0.1129 0.3607−0.5099 0.1113 0.3612 −0.5294 0.1096 0.3618 −0.5488 0.1078 0.3625−0.5682 0.1058 0.3633 −0.5875 0.1036 0.3642 −0.6069 0.1012 0.3652−0.6262 0.0986 0.3783 0.3398 0.0917 0.3798 0.3198 0.0900 0.3811 −0.21440.1262 0.3812 −0.2344 0.1256 0.3813 −0.2544 0.1250 0.3814 −0.2744 0.12430.3815 −0.2943 0.1236 0.3816 −0.3141 0.1229 0.3817 −0.3339 0.1221 0.3819−0.3536 0.1212 0.3820 −0.3733 0.1202 0.3822 −0.3929 0.1192 0.3825−0.4126 0.1181 0.3827 −0.4322 0.1169 0.3830 −0.4518 0.1156 0.3834−0.4713 0.1142 0.3838 −0.4909 0.1127 0.3842 −0.5104 0.1111 0.3847−0.5299 0.1094 0.3852 −0.5493 0.1075 0.3858 −0.5687 0.1055 0.3865−0.5882 0.1034 0.3872 −0.6076 0.1011 0.3881 −0.6270 0.0986 0.3890−0.6465 0.0960 0.4019 0.3189 0.0908 0.4048 −0.2360 0.1255 0.4048 −0.25600.1250 0.4048 −0.2760 0.1243 0.4049 −0.2959 0.1236 0.4050 −0.3157 0.12280.4052 −0.3355 0.1219 0.4054 −0.3553 0.1209 0.4056 −0.3750 0.1199 0.4058−0.3946 0.1187 0.4061 −0.4143 0.1175 0.4063 −0.4339 0.1162 0.4066−0.4535 0.1148 0.4070 −0.4731 0.1134 0.4073 −0.4927 0.1118 0.4077−0.5122 0.1102 0.4081 −0.5317 0.1085 0.4086 −0.5512 0.1067 0.4091−0.5707 0.1048 0.4096 −0.5902 0.1028 0.4102 −0.6096 0.1006 0.4109−0.6291 0.0984 0.4116 −0.6486 0.0959 0.4240 0.3167 0.0915 0.4282 −0.25900.1245 0.4282 −0.2389 0.1250 0.4282 −0.2789 0.1239 0.4283 −0.2989 0.12310.4284 −0.3187 0.1222 0.4286 −0.3385 0.1212 0.4288 −0.3583 0.1201 0.4290−0.3780 0.1189 0.4293 −0.3977 0.1176 0.4296 −0.4174 0.1163 0.4299−0.4370 0.1149 0.4302 −0.4567 0.1134 0.4305 −0.4763 0.1119 0.4308−0.4959 0.1104 0.4311 −0.5154 0.1088 0.4315 −0.5350 0.1072 0.4318−0.5545 0.1055 0.4322 −0.5740 0.1038 0.4325 −0.5935 0.1019 0.4330−0.6130 0.1000 0.4334 −0.6325 0.0980 0.4339 −0.6521 0.0958 0.4513−0.2632 0.1238 0.4514 −0.2832 0.1231 0.4515 −0.3032 0.1222 0.4516−0.3231 0.1212 0.4519 −0.3429 0.1200 0.4521 −0.3627 0.1188 0.4524−0.3824 0.1174 0.4527 −0.4021 0.1160 0.4530 −0.4218 0.1145 0.4533−0.4415 0.1130 0.4536 −0.4611 0.1115 0.4539 −0.4808 0.1100 0.4541−0.5004 0.1085 0.4544 −0.5199 0.1070 0.4546 −0.5395 0.1056 0.4548−0.5590 0.1041 0.4550 −0.5785 0.1026 0.4552 −0.5980 0.1010 0.4554−0.6175 0.0994 0.4556 −0.6371 0.0977 0.4559 −0.6566 0.0959 0.4743−0.2688 0.1229 0.4743 −0.2888 0.1221 0.4745 −0.3088 0.1210 0.4747−0.3287 0.1198 0.4750 −0.3485 0.1185 0.4753 −0.3683 0.1170 0.4756−0.3881 0.1155 0.4759 −0.4078 0.1139 0.4763 −0.4275 0.1123 0.4766−0.4472 0.1107 0.4768 −0.4669 0.1091 0.4771 −0.4865 0.1076 0.4772−0.5061 0.1062 0.4774 −0.5257 0.1049 0.4774 −0.5452 0.1037 0.4775−0.5647 0.1025 0.4775 −0.5842 0.1013 0.4775 −0.6037 0.1001 0.4775−0.6232 0.0989 0.4775 −0.6428 0.0976 0.4776 −0.6624 0.0962 0.4969−0.2756 0.1218 0.4970 −0.2956 0.1208 0.4972 −0.3156 0.1196 0.4975−0.3355 0.1182 0.4978 −0.3554 0.1166 0.4982 −0.3752 0.1149 0.4985−0.3950 0.1132 0.4988 −0.6692 0.0970 0.4989 −0.4148 0.1114 0.4990−0.6496 0.0979 0.4992 −0.6301 0.0987 0.4993 −0.4345 0.1096 0.4994−0.6106 0.0994 0.4996 −0.4542 0.1079 0.4996 −0.5911 0.1002 0.4998−0.5716 0.1009 0.4998 −0.4738 0.1064 0.4999 −0.5521 0.1018 0.5000−0.4935 0.1049 0.5000 −0.5326 0.1027 0.5000 −0.5130 0.1037 0.5194−0.3035 0.1195 0.5196 −0.3235 0.1180 0.5198 −0.6770 0.0980 0.5199−0.3435 0.1164 0.5202 −0.6575 0.0984 0.5203 −0.3634 0.1145 0.5206−0.6379 0.0987 0.5207 −0.3833 0.1126 0.5210 −0.6185 0.0989 0.5212−0.4031 0.1106 0.5214 −0.5990 0.0991 0.5216 −0.4229 0.1086 0.5218−0.5796 0.0994 0.5219 −0.4426 0.1067 0.5221 −0.5601 0.0997 0.5222−0.4623 0.1049 0.5223 −0.5406 0.1003 0.5224 −0.4819 0.1034 0.5225−0.5211 0.1010 0.5225 −0.5015 0.1020 0.5404 −0.6858 0.0992 0.5410−0.6663 0.0991 0.5414 −0.3125 0.1179 0.5416 −0.6468 0.0988 0.5417−0.3326 0.1163 0.5421 −0.3526 0.1143 0.5422 −0.6274 0.0984 0.5425−0.3725 0.1122 0.5428 −0.6079 0.0981 0.5430 −0.3924 0.1100 0.5433−0.5885 0.0978 0.5434 −0.4122 0.1078 0.5438 −0.5691 0.0977 0.5439−0.4320 0.1056 0.5442 −0.4518 0.1035 0.5442 −0.5497 0.0978 0.5445−0.4715 0.1017 0.5445 −0.5302 0.0982 0.5447 −0.4911 0.1002 0.5447−0.5107 0.0990 0.5608 −0.6956 0.1005 0.5615 −0.6761 0.0998 0.5623−0.6567 0.0990 0.5630 −0.6372 0.0981 0.5632 −0.3226 0.1163 0.5635−0.3427 0.1144 0.5638 −0.6179 0.0972 0.5639 −0.3627 0.1121 0.5644−0.3827 0.1098 0.5645 −0.5985 0.0963 0.5648 −0.4026 0.1073 0.5651−0.5791 0.0957 0.5653 −0.4224 0.1048 0.5657 −0.5597 0.0954 0.5657−0.4422 0.1024 0.5660 −0.4619 0.1003 0.5661 −0.5403 0.0954 0.5663−0.4816 0.0984 0.5663 −0.5208 0.0959 0.5664 −0.5012 0.0969 0.5819−0.6869 0.1006 0.5827 −0.6675 0.0992 0.5836 −0.6481 0.0977 0.5844−0.6287 0.0962 0.5847 −0.3338 0.1145 0.5850 −0.3538 0.1123 0.5852−0.6093 0.0949 0.5854 −0.3738 0.1098 0.5858 −0.3938 0.1071 0.5859−0.5900 0.0937 0.5862 −0.4137 0.1044 0.5865 −0.5706 0.0929 0.5866−0.4335 0.1017 0.5870 −0.4533 0.0992 0.5870 −0.5512 0.0925 0.5873−0.4730 0.0969 0.5873 −0.5317 0.0927 0.5874 −0.4926 0.0950 0.5875−0.5122 0.0936 0.6021 −0.6987 0.1013 0.6029 −0.6792 0.0994 0.6037−0.6597 0.0973 0.6046 −0.6403 0.0953 0.6054 −0.6210 0.0933 0.6060−0.3659 0.1100 0.6061 −0.6016 0.0917 0.6063 −0.3858 0.1073 0.6066−0.4057 0.1043 0.6067 −0.5822 0.0904 0.6070 −0.4256 0.1014 0.6072−0.5628 0.0896 0.6073 −0.4454 0.0985 0.6076 −0.4651 0.0958 0.6076−0.5434 0.0895 0.6078 −0.4847 0.0935 0.6078 −0.5239 0.0902 0.6079−0.5043 0.0916 0.6221 −0.7114 0.1017 0.6229 −0.6918 0.0993 0.6236−0.6722 0.0968 0.6243 −0.6527 0.0942 0.6250 −0.6333 0.0917 0.6257−0.6138 0.0896 0.6262 −0.5944 0.0879 0.6264 −0.3786 0.1075 0.6266−0.3985 0.1045 0.6267 −0.5749 0.0867 0.6268 −0.4183 0.1014 0.6270−0.4381 0.0982 0.6271 −0.5555 0.0864 0.6272 −0.4578 0.0952 0.6273−0.5360 0.0868 0.6274 −0.4774 0.0924 0.6274 −0.5165 0.0881 0.6274−0.4970 0.0900 0.6426 −0.7052 0.0990 0.6431 −0.6855 0.0960 0.6436−0.6658 0.0930 0.6441 −0.6461 0.0901 0.6446 −0.6265 0.0875 0.6450−0.6070 0.0853 0.6454 −0.5875 0.0839 0.6457 −0.5680 0.0832 0.6460−0.5485 0.0835 0.6461 −0.5290 0.0846 0.6462 −0.5096 0.0864 0.6462−0.3920 0.1048 0.6463 −0.4118 0.1016 0.6463 −0.4314 0.0982 0.6463−0.4901 0.0889 0.6463 −0.4510 0.0949 0.6463 −0.4706 0.0917 0.6523 0.26340.1102 0.6620 −0.7194 0.0984 0.6622 −0.6994 0.0950 0.6624 −0.6794 0.09160.6626 −0.6595 0.0883 0.6628 −0.6397 0.0853 0.6631 −0.6199 0.0828 0.6633−0.6003 0.0810 0.6635 −0.5807 0.0801 0.6637 −0.5612 0.0802 0.6639−0.5417 0.0812 0.6641 −0.5224 0.0830 0.6643 −0.5030 0.0854 0.6645−0.4837 0.0883 0.6647 −0.4643 0.0915 0.6649 −0.4449 0.0949 0.6651−0.4254 0.0984 0.6653 −0.4058 0.1018 0.6723 0.2488 0.1115 0.6804 −0.61330.0783 0.6804 −0.6332 0.0803 0.6804 −0.5936 0.0771 0.6805 −0.6532 0.08310.6806 −0.5740 0.0770 0.6806 −0.6734 0.0864 0.6808 −0.6936 0.0900 0.6808−0.5546 0.0779 0.6809 −0.7139 0.0938 0.6811 −0.5353 0.0795 0.6814−0.5161 0.0819 0.6818 −0.4969 0.0848 0.6823 −0.4777 0.0881 0.6827−0.4585 0.0915 0.6832 −0.4393 0.0951 0.6836 −0.4200 0.0986 0.6919 0.25280.1077 0.6968 −0.6067 0.0743 0.6968 −0.5871 0.0740 0.6969 −0.6266 0.07560.6970 −0.5676 0.0747 0.6972 −0.6468 0.0779 0.6974 −0.5484 0.0763 0.6976−0.6671 0.0809 0.6978 −0.5293 0.0785 0.6981 −0.6876 0.0844 0.6984−0.5103 0.0813 0.6986 −0.7082 0.0883 0.6990 −0.4913 0.0846 0.6992−0.7290 0.0922 0.6997 −0.4724 0.0881 0.7004 −0.4533 0.0917 0.7110 0.23690.1079 0.7126 −0.6005 0.0712 0.7127 −0.6202 0.0716 0.7128 −0.5810 0.07170.7130 −0.6403 0.0732 0.7131 −0.5618 0.0731 0.7135 −0.6607 0.0756 0.7137−0.5428 0.0753 0.7142 −0.6814 0.0787 0.7144 −0.5239 0.0780 0.7150−0.7023 0.0824 0.7152 −0.5051 0.0811 0.7159 −0.7233 0.0864 0.7160−0.4863 0.0845 0.7169 −0.4676 0.0881 0.7281 −0.6144 0.0686 0.7283−0.5948 0.0690 0.7283 −0.6343 0.0692 0.7285 0.2405 0.1023 0.7286 −0.57560.0703 0.7288 −0.6546 0.0709 0.7292 −0.5566 0.0722 0.7294 0.2204 0.10780.7295 −0.6752 0.0734 0.7299 −0.5379 0.0748 0.7305 −0.6962 0.0767 0.7308−0.5192 0.0778 0.7316 −0.7174 0.0804 0.7318 −0.5006 0.0811 0.7328−0.7388 0.0844 0.7328 −0.4820 0.0846 0.7435 −0.6289 0.0664 0.7435−0.6093 0.0666 0.7438 −0.6489 0.0671 0.7439 −0.5900 0.0677 0.7444−0.5710 0.0694 0.7444 −0.6694 0.0689 0.7451 −0.5523 0.0718 0.7453−0.6903 0.0715 0.7459 0.2241 0.1017 0.7461 −0.5337 0.0746 0.7464 −0.71150.0747 0.7471 0.2036 0.1072 0.7471 −0.5151 0.0777 0.7477 −0.7329 0.07840.7482 −0.4967 0.0811 0.7587 −0.6242 0.0645 0.7587 −0.6440 0.0644 0.7589−0.6049 0.0653 0.7591 −0.6641 0.0653 0.7594 −0.5859 0.0669 0.7598−0.6848 0.0671 0.7601 −0.5671 0.0690 0.7608 −0.7058 0.0697 0.7610−0.5485 0.0716 0.7612 0.2280 0.0952 0.7620 −0.5300 0.0745 0.7621 −0.72720.0728 0.7626 0.2074 0.1010 0.7631 −0.5116 0.0777 0.7635 −0.7489 0.07650.7639 0.1867 0.1064 0.7736 −0.6397 0.0626 0.7738 −0.6596 0.0627 0.7738−0.6203 0.0632 0.7742 −0.6012 0.0645 0.7742 −0.6799 0.0636 0.7748−0.5823 0.0664 0.7750 −0.7006 0.0655 0.7757 −0.5637 0.0687 0.7761−0.7218 0.0680 0.7766 −0.5452 0.0714 0.7772 0.2114 0.0945 0.7774 −0.74330.0711 0.7777 −0.5268 0.0744 0.7787 0.1905 0.1001 0.7801 0.1696 0.10530.7884 −0.6557 0.0609 0.7885 −0.6362 0.0614 0.7886 −0.6757 0.0612 0.7888−0.6169 0.0624 0.7891 −0.6961 0.0622 0.7893 −0.5980 0.0640 0.7900−0.7169 0.0640 0.7901 −0.5792 0.0661 0.7909 −0.5607 0.0685 0.7911−0.7382 0.0665 0.7911 0.2155 0.0881 0.7920 −0.5422 0.0713 0.7927 0.19460.0936 0.7942 0.1735 0.0991 0.7956 0.1525 0.1041 0.8030 −0.6525 0.05970.8030 −0.6722 0.0594 0.8032 −0.6332 0.0605 0.8033 −0.6923 0.0598 0.8037−0.6141 0.0618 0.8039 −0.7128 0.0609 0.8043 −0.5952 0.0636 0.8045 0.21960.0821 0.8047 −0.7337 0.0627 0.8050 −0.5765 0.0658 0.8058 −0.7550 0.06510.8060 −0.5580 0.0683 0.8060 0.1987 0.0875 0.8076 0.1776 0.0928 0.80910.1565 0.0980 0.8174 −0.6694 0.0582 0.8175 −0.6892 0.0581 0.8175 −0.64990.0587 0.8178 −0.7094 0.0586 0.8178 −0.6307 0.0598 0.8183 −0.6117 0.06130.8184 −0.7300 0.0598 0.8189 −0.5928 0.0633 0.8191 0.2026 0.0818 0.8192−0.7509 0.0615 0.8197 −0.5742 0.0655 0.8206 0.1816 0.0869 0.8207 −0.55570.0681 0.8220 0.1605 0.0920 0.8234 0.1394 0.0969 0.8314 −0.6866 0.05680.8315 −0.6669 0.0572 0.8316 −0.7065 0.0569 0.8317 −0.6476 0.0580 0.8320−0.7268 0.0576 0.8320 −0.6284 0.0592 0.8320 0.2062 0.0769 0.8325 −0.74740.0588 0.8326 −0.6095 0.0609 0.8332 −0.5907 0.0629 0.8333 0.1853 0.08160.8341 −0.5720 0.0653 0.8346 0.1643 0.0865 0.8360 0.1433 0.0912 0.83720.1223 0.0958 0.8449 0.2094 0.0727 0.8451 −0.6843 0.0558 0.8451 −0.70400.0556 0.8452 −0.6647 0.0563 0.8453 −0.7241 0.0559 0.8454 −0.6454 0.05730.8457 −0.7445 0.0566 0.8459 −0.6263 0.0587 0.8460 0.1887 0.0770 0.8463−0.7651 0.0579 0.8464 −0.6074 0.0605 0.8471 −0.5887 0.0627 0.8471 0.16780.0815 0.8483 0.1469 0.0860 0.8495 0.1260 0.0905 0.8506 0.1051 0.09470.8583 −0.7018 0.0545 0.8583 −0.6821 0.0548 0.8585 −0.7217 0.0545 0.8585−0.6626 0.0555 0.8586 0.1916 0.0732 0.8587 −0.7419 0.0550 0.8588 −0.64340.0567 0.8591 −0.7623 0.0558 0.8593 −0.6243 0.0582 0.8595 0.1709 0.07720.8599 −0.6055 0.0602 0.8606 0.1502 0.0814 0.8616 0.1294 0.0856 0.86270.1085 0.0897 0.8636 0.0877 0.0936 0.8710 0.1942 0.0700 0.8712 −0.69960.0534 0.8713 −0.7195 0.0533 0.8713 −0.6800 0.0539 0.8715 −0.7395 0.05350.8715 −0.6606 0.0548 0.8718 −0.7598 0.0541 0.8719 0.1737 0.0736 0.8719−0.6415 0.0561 0.8724 −0.6225 0.0579 0.8727 0.1531 0.0775 0.8737 0.13240.0814 0.8746 0.1117 0.0853 0.8755 0.0909 0.0890 0.8763 0.0702 0.09260.8834 0.1966 0.0673 0.8838 −0.7173 0.0521 0.8838 −0.6976 0.0524 0.8839−0.7373 0.0521 0.8839 −0.6781 0.0530 0.8841 0.1762 0.0706 0.8841 −0.75750.0525 0.8842 −0.6588 0.0542 0.8845 −0.7779 0.0533 0.8847 −0.6397 0.05580.8848 0.1557 0.0741 0.8853 −0.6209 0.0579 0.8856 0.1351 0.0777 0.88640.1145 0.0814 0.8872 0.0939 0.0849 0.8880 0.0732 0.0883 0.8887 0.05260.0915 0.8960 −0.7153 0.0509 0.8960 −0.7352 0.0508 0.8960 −0.6956 0.05140.8961 0.1784 0.0681 0.8962 −0.7553 0.0511 0.8963 −0.6762 0.0523 0.8965−0.7756 0.0516 0.8967 −0.6570 0.0538 0.8967 0.1580 0.0713 0.8972 −0.63810.0557 0.8974 0.1376 0.0746 0.8981 0.1171 0.0780 0.8988 0.0965 0.08130.8995 0.0760 0.0846 0.9001 0.0555 0.0877 0.9007 0.0350 0.0905 0.9079−0.7331 0.0496 0.9079 −0.7133 0.0499 0.9080 0.1805 0.0660 0.9080 −0.75310.0496 0.9081 −0.6938 0.0506 0.9083 −0.7734 0.0500 0.9084 −0.6745 0.05190.9085 0.1602 0.0689 0.9089 −0.6555 0.0537 0.9091 0.1398 0.0720 0.90970.1194 0.0751 0.9103 0.0989 0.0782 0.9109 0.0785 0.0813 0.9115 0.05800.0843 0.9120 0.0376 0.0870 0.9125 0.0172 0.0895 0.9195 −0.7312 0.04840.9196 −0.7511 0.0483 0.9196 0.1824 0.0639 0.9196 −0.7115 0.0490 0.9198−0.7712 0.0485 0.9199 −0.6922 0.0501 0.9201 0.1621 0.0668 0.9204 −0.67310.0519 0.9206 0.1418 0.0697 0.9212 0.1214 0.0726 0.9217 0.1010 0.07560.9222 0.0807 0.0785 0.9228 0.0603 0.0813 0.9232 0.0399 0.0839 0.92370.0196 0.0864 0.9240 −0.0007 0.0885 0.9309 −0.7492 0.0471 0.9310 −0.72950.0475 0.9310 −0.7692 0.0470 0.9310 0.1842 0.0619 0.9312 −0.7100 0.04850.9312 −0.7895 0.0474 0.9314 0.1640 0.0647 0.9316 −0.6909 0.0501 0.93190.1437 0.0675 0.9324 0.1233 0.0704 0.9329 0.1030 0.0732 0.9334 0.08260.0760 0.9339 0.0623 0.0787 0.9343 0.0420 0.0812 0.9347 0.0217 0.08360.9350 0.0015 0.0857 0.9353 −0.0187 0.0876 0.9420 −0.7674 0.0458 0.9420−0.7476 0.0461 0.9422 −0.7875 0.0458 0.9422 −0.7280 0.0470 0.9425 0.16570.0626 0.9426 −0.7088 0.0485 0.9430 0.1454 0.0654 0.9434 0.1251 0.06820.9439 0.1047 0.0711 0.9444 0.0844 0.0738 0.9448 0.0640 0.0764 0.94520.0438 0.0789 0.9456 0.0235 0.0812 0.9459 0.0033 0.0832 0.9462 −0.01680.0850 0.9530 −0.7659 0.0448 0.9530 −0.7858 0.0445 0.9531 −0.7462 0.04550.9534 0.1674 0.0606 0.9534 −0.7270 0.0470 0.9538 0.1471 0.0633 0.9540−0.7082 0.0491 0.9542 0.1268 0.0661 0.9547 0.1064 0.0689 0.9552 0.08600.0717 0.9556 0.0657 0.0743 0.9560 0.0454 0.0768 0.9563 0.0251 0.07900.9566 0.0050 0.0810 0.9569 −0.0151 0.0828 0.9570 −0.0351 0.0844 0.9637−0.7843 0.0435 0.9638 −0.7646 0.0442 0.9640 0.1690 0.0586 0.9641 −0.74530.0455 0.9644 0.1487 0.0612 0.9646 −0.7264 0.0476 0.9648 0.1284 0.06390.9653 0.1080 0.0668 0.9658 0.0876 0.0696 0.9662 0.0672 0.0723 0.96660.0468 0.0748 0.9669 0.0266 0.0771 0.9672 0.0064 0.0791 0.9674 −0.01370.0809 0.9676 −0.0336 0.0824 0.9677 −0.0535 0.0836 0.9742 −0.8028 0.04230.9743 −0.7831 0.0430 0.9745 0.1704 0.0568 0.9746 −0.7637 0.0442 0.97480.1503 0.0592 0.9751 −0.7448 0.0462 0.9752 0.1300 0.0618 0.9756 0.10960.0646 0.9761 0.0891 0.0674 0.9766 0.0687 0.0702 0.9770 0.0483 0.07280.9774 0.0280 0.0752 0.9777 0.0077 0.0773 0.9779 −0.0123 0.0791 0.9780−0.0323 0.0806 0.9781 −0.0522 0.0819 0.9782 −0.0720 0.0829 0.9846−0.8016 0.0418 0.9849 −0.7822 0.0430 0.9851 0.1517 0.0573 0.9853 −0.76330.0450 0.9854 0.1315 0.0598 0.9858 0.1111 0.0624 0.9863 0.0907 0.06520.9867 0.0702 0.0681 0.9872 0.0497 0.0708 0.9876 0.0293 0.0733 0.98790.0090 0.0755 0.9882 −0.0111 0.0774 0.9883 −0.0312 0.0790 0.9884 −0.05110.0803 0.9884 −0.0906 0.0821 0.9885 −0.0709 0.0814 0.9950 −0.8009 0.04190.9952 0.1530 0.0558 0.9955 −0.7819 0.0438 0.9955 0.1329 0.0579 0.99580.1126 0.0604 0.9962 0.0922 0.0631 0.9967 0.0717 0.0658 0.9971 0.05120.0686 0.9976 0.0307 0.0712 0.9980 0.0103 0.0736 0.9983 −0.0099 0.07570.9985 −0.0301 0.0774 0.9985 −0.1092 0.0813 0.9986 −0.0500 0.0788 0.9986−0.0896 0.0807 0.9986 −0.0699 0.0799 1.0053 0.1541 0.0547 1.0054 −0.80070.0426 1.0054 0.1341 0.0565 1.0057 0.1139 0.0586 1.0061 0.0936 0.06111.0065 0.0731 0.0637 1.0069 0.0526 0.0664 1.0074 0.0321 0.0691 1.00780.0116 0.0716 1.0081 −0.0088 0.0739 1.0084 −0.0290 0.0758 1.0084 −0.12800.0805 1.0085 −0.0491 0.0773 1.0086 −0.1084 0.0801 1.0086 −0.0690 0.07851.0086 −0.0887 0.0794 1.0154 0.1351 0.0554 1.0154 0.1549 0.0542 1.01550.1150 0.0572 1.0158 0.0948 0.0593 1.0161 0.0744 0.0617 1.0165 0.05390.0643 1.0170 0.0334 0.0670 1.0174 0.0129 0.0695 1.0178 −0.0076 0.07191.0181 −0.0280 0.0740 1.0182 −0.1468 0.0796 1.0183 −0.0481 0.0758 1.0183−0.1273 0.0794 1.0184 −0.0682 0.0771 1.0184 −0.1077 0.0789 1.0185−0.0880 0.0782 1.0252 0.1358 0.0549 1.0253 0.1159 0.0562 1.0254 0.09580.0580 1.0254 0.1554 0.0543 1.0257 0.0755 0.0601 1.0260 0.0551 0.06241.0264 0.0346 0.0649 1.0268 0.0141 0.0675 1.0272 −0.0065 0.0699 1.0276−0.0269 0.0722 1.0277 −0.1657 0.0787 1.0278 −0.0472 0.0741 1.0279−0.1463 0.0786 1.0280 −0.0674 0.0757 1.0280 −0.1268 0.0783 1.0281−0.0873 0.0769 1.0281 −0.1071 0.0777 1.0350 0.1165 0.0558 1.0350 0.09650.0570 1.0351 0.1361 0.0550 1.0351 0.0764 0.0588 1.0354 0.0561 0.06081.0357 0.0357 0.0631 1.0361 0.0152 0.0655 1.0365 −0.0053 0.0679 1.0369−0.0259 0.0702 1.0371 −0.1847 0.0777 1.0372 −0.0463 0.0723 1.0373−0.1653 0.0778 1.0374 −0.0666 0.0741 1.0375 −0.1459 0.0776 1.0376−0.0867 0.0755 1.0376 −0.1263 0.0772 1.0376 −0.1066 0.0765 1.0445 0.09710.0566 1.0445 0.0771 0.0579 1.0446 0.1168 0.0558 1.0447 0.0570 0.05961.0449 0.0367 0.0616 1.0450 0.1363 0.0557 1.0453 0.0162 0.0637 1.0456−0.0043 0.0660 1.0460 −0.0248 0.0683 1.0463 −0.2037 0.0768 1.0463−0.0453 0.0704 1.0466 −0.1844 0.0770 1.0466 −0.0657 0.0724 1.0468−0.1650 0.0769 1.0468 −0.0859 0.0740 1.0469 −0.1455 0.0767 1.0470−0.1060 0.0752 1.0470 −0.1258 0.0761 1.0540 0.0776 0.0575 1.0540 0.05770.0587 1.0541 0.0974 0.0567 1.0541 0.0375 0.0604 1.0543 0.1169 0.05651.0544 0.0171 0.0623 1.0547 −0.0033 0.0643 1.0548 0.1361 0.0569 1.0550−0.0238 0.0665 1.0554 −0.0443 0.0686 1.0554 −0.2227 0.0758 1.0557−0.0647 0.0706 1.0557 −0.2035 0.0761 1.0559 −0.1841 0.0762 1.0559−0.0851 0.0723 1.0561 −0.1647 0.0760 1.0561 −0.1053 0.0738 1.0562−0.1451 0.0756 1.0562 −0.1253 0.0749 1.0633 0.0580 0.0584 1.0633 0.03800.0596 1.0634 0.0778 0.0576 1.0635 0.0178 0.0611 1.0636 0.0974 0.05731.0637 −0.0025 0.0629 1.0640 −0.0229 0.0649 1.0641 0.1166 0.0576 1.0643−0.0434 0.0669 1.0644 −0.2418 0.0748 1.0646 −0.0638 0.0688 1.0647−0.2226 0.0751 1.0648 0.1355 0.0587 1.0649 −0.0842 0.0706 1.0649 −0.20330.0753 1.0651 −0.1045 0.0722 1.0651 −0.1839 0.0753 1.0652 −0.1643 0.07501.0652 −0.1247 0.0735 1.0653 −0.1446 0.0744 1.0725 0.0383 0.0592 1.07250.0183 0.0604 1.0726 0.0582 0.0584 1.0727 −0.0019 0.0619 1.0728 0.07770.0581 1.0729 −0.0222 0.0636 1.0731 −0.0426 0.0654 1.0732 −0.2609 0.07371.0732 0.0970 0.0583 1.0734 −0.0630 0.0672 1.0735 −0.2417 0.0742 1.0736−0.0834 0.0690 1.0737 −0.2225 0.0745 1.0738 0.1160 0.0592 1.0739 −0.10380.0706 1.0740 −0.2032 0.0746 1.0741 −0.1240 0.0720 1.0741 −0.1837 0.07441.0742 −0.1441 0.0732 1.0742 −0.1640 0.0739 1.0747 0.1346 0.0608 1.08150.0186 0.0600 1.0816 −0.0015 0.0612 1.0816 0.0384 0.0593 1.0817 −0.02170.0625 1.0818 0.0581 0.0589 1.0819 −0.0419 0.0641 1.0819 −0.2801 0.07271.0821 −0.0623 0.0658 1.0822 −0.2610 0.0732 1.0822 0.0774 0.0591 1.0823−0.0827 0.0674 1.0825 −0.2418 0.0736 1.0826 −0.1031 0.0690 1.0827−0.2225 0.0737 1.0828 −0.1234 0.0705 1.0828 0.0964 0.0598 1.0829 −0.20300.0737 1.0829 −0.1436 0.0718 1.0830 −0.1834 0.0734 1.0830 −0.1636 0.07271.0835 0.1151 0.0612 1.0845 0.1335 0.0630 1.0904 −0.0013 0.0608 1.0904−0.2994 0.0716 1.0904 −0.0213 0.0619 1.0905 0.0186 0.0601 1.0906 −0.04150.0631 1.0907 0.0383 0.0597 1.0907 −0.0618 0.0646 1.0908 −0.2803 0.07221.0909 −0.0821 0.0661 1.0910 −0.2611 0.0726 1.0910 0.0577 0.0597 1.0911−0.1024 0.0676 1.0913 −0.2419 0.0729 1.0913 −0.1228 0.0690 1.0915−0.2225 0.0729 1.0915 −0.1430 0.0703 1.0916 0.0768 0.0603 1.0916 −0.20290.0727 1.0916 −0.1632 0.0714 1.0917 −0.1831 0.0722 1.0923 0.0956 0.06151.0931 0.1140 0.0631 1.0941 0.1322 0.0651 1.0989 −0.3187 0.0705 1.0992−0.2996 0.0711 1.0992 −0.0212 0.0615 1.0992 −0.0412 0.0625 1.0993−0.0013 0.0608 1.0993 −0.0614 0.0637 1.0995 −0.0816 0.0649 1.0995 0.01840.0604 1.0995 −0.2805 0.0716 1.0996 −0.1019 0.0663 1.0998 −0.2613 0.07201.0998 0.0379 0.0604 1.0998 −0.1222 0.0676 1.1000 −0.1425 0.0689 1.1000−0.2419 0.0721 1.1001 −0.1627 0.0700 1.1001 −0.2224 0.0720 1.1002−0.1828 0.0710 1.1002 −0.2027 0.0716 1.1003 0.0571 0.0609 1.1009 0.07590.0619 1.1017 0.0945 0.0633 1.1026 0.1128 0.0650 1.1036 0.1310 0.06691.1069 −0.3570 0.0687 1.1072 −0.3379 0.0694 1.1076 −0.3189 0.0701 1.1079−0.2998 0.0706 1.1079 −0.0413 0.0621 1.1079 −0.0613 0.0630 1.1080−0.0214 0.0614 1.1080 −0.0814 0.0641 1.1081 −0.1016 0.0652 1.1082−0.2806 0.0710 1.1082 −0.0016 0.0610 1.1082 −0.1218 0.0664 1.1084−0.2613 0.0712 1.1084 −0.1420 0.0676 1.1085 0.0179 0.0610 1.1085 −0.16220.0687 1.1085 −0.2418 0.0712 1.1086 −0.1823 0.0697 1.1086 −0.2222 0.07101.1087 −0.2023 0.0704 1.1089 0.0371 0.0614 1.1095 0.0561 0.0622 1.11020.0748 0.0633 1.1110 0.0934 0.0648 1.1119 0.1117 0.0664 1.1128 0.13000.0682 1.1153 −0.3759 0.0676 1.1157 −0.3569 0.0683 1.1160 −0.3378 0.06901.1163 −0.3187 0.0695 1.1166 −0.2995 0.0700 1.1167 −0.0811 0.0634 1.1167−0.0611 0.0626 1.1167 −0.1011 0.0644 1.1167 −0.0412 0.0620 1.1168−0.1212 0.0654 1.1168 −0.2802 0.0703 1.1169 −0.1414 0.0664 1.1169−0.0215 0.0616 1.1170 −0.1615 0.0674 1.1170 −0.2608 0.0704 1.1171−0.1816 0.0684 1.1171 −0.2412 0.0702 1.1172 −0.2016 0.0692 1.1172−0.2215 0.0698 1.1172 −0.0019 0.0615 1.1176 0.0175 0.0618 1.1181 0.03660.0624 1.1188 0.0555 0.0634 1.1195 0.0742 0.0646 1.1203 0.0928 0.06601.1211 0.1113 0.0674 1.1220 0.1299 0.0689 1.1239 −0.3942 0.0664 1.1243−0.3751 0.0671 1.1246 −0.3560 0.0678 1.1249 −0.3369 0.0684 1.1252−0.3178 0.0689 1.1254 −0.2985 0.0693 1.1255 −0.1001 0.0637 1.1256−0.0801 0.0630 1.1256 −0.1201 0.0646 1.1256 −0.1401 0.0654 1.1256−0.2791 0.0694 1.1256 −0.0603 0.0624 1.1257 −0.1601 0.0663 1.1258−0.2596 0.0694 1.1258 −0.1802 0.0672 1.1258 −0.0405 0.0621 1.1258−0.2002 0.0680 1.1258 −0.2399 0.0691 1.1258 −0.2201 0.0686 1.1261−0.0209 0.0620 1.1264 −0.0014 0.0621 1.1269 0.0178 0.0626 1.1275 0.03680.0634 1.1281 0.0557 0.0644 1.1289 0.0745 0.0655 1.1296 0.0932 0.06671.1304 0.1119 0.0679 1.1325 −0.4124 0.0652 1.1328 −0.3933 0.0660 1.1331−0.3742 0.0667 1.1334 −0.3551 0.0673 1.1337 −0.3359 0.0678 1.1340−0.3167 0.0682 1.1342 −0.2973 0.0684 1.1343 −0.2779 0.0685 1.1344−0.1389 0.0646 1.1344 −0.1189 0.0639 1.1344 −0.1588 0.0653 1.1344−0.0990 0.0633 1.1344 −0.1788 0.0661 1.1344 −0.2582 0.0683 1.1345−0.1987 0.0668 1.1345 −0.2385 0.0679 1.1345 −0.2186 0.0674 1.1345−0.0792 0.0628 1.1346 −0.0594 0.0624 1.1349 −0.0397 0.0623 1.1352−0.0202 0.0624 1.1356 −0.0009 0.0628 1.1362 0.0183 0.0634 1.1368 0.03730.0642 1.1374 0.0562 0.0651 1.1380 0.0751 0.0660 1.1387 0.0940 0.06691.1394 0.1129 0.0678 1.1408 −0.4493 0.0633 1.1411 −0.4301 0.0641 1.1415−0.4110 0.0648 1.1418 −0.3919 0.0655 1.1421 −0.3728 0.0661 1.1424−0.3536 0.0667 1.1426 −0.3344 0.0671 1.1428 −0.3151 0.0674 1.1430−0.2956 0.0675 1.1431 −0.2760 0.0674 1.1432 −0.2564 0.0672 1.1432−0.2366 0.0668 1.1432 −0.1771 0.0651 1.1432 −0.1970 0.0657 1.1432−0.1572 0.0645 1.1432 −0.2168 0.0663 1.1433 −0.1374 0.0639 1.1433−0.1175 0.0634 1.1434 −0.0977 0.0630 1.1436 −0.0779 0.0627 1.1438−0.0583 0.0625 1.1441 −0.0387 0.0626 1.1445 −0.0192 0.0629 1.1450 0.00010.0633 1.1455 0.0192 0.0639 1.1461 0.0384 0.0646 1.1466 0.0574 0.06531.1472 0.0765 0.0661 1.1478 0.0956 0.0667 1.1484 0.1148 0.0673 1.1500−0.4658 0.0622 1.1503 −0.4466 0.0629 1.1506 −0.4275 0.0636 1.1509−0.4083 0.0643 1.1512 −0.3892 0.0649 1.1515 −0.3700 0.0655 1.1517−0.3507 0.0659 1.1519 −0.3314 0.0662 1.1521 −0.3120 0.0664 1.1522−0.2925 0.0664 1.1523 −0.2729 0.0663 1.1524 −0.2532 0.0660 1.1524−0.2335 0.0657 1.1525 −0.2138 0.0652 1.1525 −0.1940 0.0648 1.1525−0.1742 0.0643 1.1526 −0.1544 0.0638 1.1526 −0.1346 0.0634 1.1528−0.1149 0.0630 1.1529 −0.0951 0.0627 1.1531 −0.0754 0.0626 1.1534−0.0558 0.0626 1.1538 −0.0362 0.0628 1.1542 −0.0168 0.0632 1.1547 0.00250.0636 1.1552 0.0218 0.0641 1.1557 0.0410 0.0647 1.1562 0.0603 0.06521.1568 0.0795 0.0657 1.1568 −0.8556 0.0493 1.1573 0.0988 0.0661 1.15780.1182 0.0664 1.1589 −0.5013 0.0603 1.1592 −0.4820 0.0610 1.1594 −0.46280.0617 1.1597 −0.4436 0.0624 1.1600 −0.4244 0.0631 1.1603 −0.4053 0.06371.1606 −0.3861 0.0643 1.1608 −0.3668 0.0647 1.1610 −0.3475 0.0650 1.1612−0.3281 0.0653 1.1614 −0.3086 0.0653 1.1615 −0.2891 0.0653 1.1616−0.2694 0.0651 1.1616 −0.2498 0.0649 1.1617 −0.2301 0.0646 1.1617−0.2103 0.0642 1.1618 −0.1906 0.0639 1.1619 −0.1708 0.0635 1.1620−0.1511 0.0632 1.1621 −0.1313 0.0629 1.1623 −0.1116 0.0627 1.1625−0.0919 0.0625 1.1628 −0.0722 0.0626 1.1631 −0.0527 0.0627 1.1635−0.0332 0.0629 1.1639 −0.0138 0.0633 1.1644 0.0055 0.0637 1.1648 0.02480.0641 1.1653 0.0441 0.0644 1.1656 −0.8528 0.0481 1.1658 0.0634 0.06481.1662 0.0827 0.0651 1.1667 0.1021 0.0652 1.1677 −0.5183 0.0591 1.1679−0.4990 0.0598 1.1682 −0.4797 0.0605 1.1685 −0.4606 0.0612 1.1687−0.4414 0.0619 1.1690 −0.4222 0.0625 1.1693 −0.4030 0.0630 1.1695−0.3838 0.0635 1.1697 −0.3645 0.0639 1.1699 −0.3451 0.0641 1.1701−0.3256 0.0643 1.1702 −0.3061 0.0643 1.1703 −0.2865 0.0642 1.1704−0.2668 0.0641 1.1705 −0.2471 0.0639 1.1706 −0.2275 0.0637 1.1707−0.2077 0.0634 1.1708 −0.1880 0.0631 1.1709 −0.1683 0.0629 1.1710−0.1485 0.0627 1.1712 −0.1288 0.0625 1.1714 −0.1091 0.0624 1.1717−0.0894 0.0624 1.1720 −0.0698 0.0625 1.1723 −0.0503 0.0627 1.1727−0.0309 0.0629 1.1731 −0.0116 0.0632 1.1735 0.0078 0.0635 1.1739 −0.85040.0467 1.1740 0.0271 0.0638 1.1744 0.0464 0.0640 1.1748 0.0658 0.06411.1752 0.0852 0.0642 1.1756 0.1047 0.0641 1.1759 −0.5553 0.0572 1.1761−0.5359 0.0579 1.1764 −0.5166 0.0586 1.1766 −0.4974 0.0593 1.1769−0.4781 0.0600 1.1772 −0.4590 0.0607 1.1774 −0.4398 0.0613 1.1777−0.4206 0.0618 1.1779 −0.4013 0.0623 1.1781 −0.3820 0.0627 1.1783−0.3626 0.0630 1.1785 −0.3432 0.0632 1.1786 −0.3236 0.0633 1.1788−0.3041 0.0633 1.1789 −0.2845 0.0633 1.1790 −0.2649 0.0632 1.1791−0.2452 0.0630 1.1792 −0.2256 0.0629 1.1793 −0.2059 0.0627 1.1795−0.1862 0.0625 1.1796 −0.1665 0.0624 1.1798 −0.1467 0.0623 1.1800−0.1270 0.0622 1.1803 −0.1074 0.0622 1.1806 −0.0877 0.0623 1.1809−0.0682 0.0624 1.1812 −0.0487 0.0626 1.1816 −0.0293 0.0628 1.1820−0.0099 0.0630 1.1823 −0.8475 0.0454 1.1823 0.0095 0.0631 1.1827 0.02890.0632 1.1831 0.0484 0.0633 1.1834 0.0679 0.0633 1.1838 0.0874 0.06321.1840 0.1069 0.0629 1.1844 −0.5727 0.0560 1.1846 −0.5533 0.0567 1.1849−0.5340 0.0574 1.1851 −0.5147 0.0581 1.1854 −0.4955 0.0588 1.1856−0.4763 0.0594 1.1859 −0.4570 0.0600 1.1861 −0.4378 0.0606 1.1863−0.4186 0.0610 1.1865 −0.3992 0.0614 1.1867 −0.3799 0.0618 1.1869−0.3604 0.0620 1.1871 −0.3410 0.0622 1.1872 −0.3215 0.0623 1.1874−0.3019 0.0624 1.1875 −0.2824 0.0624 1.1876 −0.2628 0.0624 1.1878−0.2432 0.0623 1.1879 −0.2235 0.0622 1.1881 −0.2039 0.0621 1.1882−0.1842 0.0621 1.1884 −0.1645 0.0620 1.1886 −0.1448 0.0620 1.1889−0.1251 0.0620 1.1891 −0.1054 0.0620 1.1894 −0.0858 0.0621 1.1897−0.0662 0.0622 1.1901 −0.0467 0.0623 1.1904 −0.0272 0.0624 1.1907−0.8638 0.0430 1.1907 −0.0078 0.0624 1.1908 −0.8442 0.0441 1.1911 0.01170.0625 1.1914 0.0312 0.0624 1.1917 0.0508 0.0624 1.1920 0.0704 0.06221.1923 0.0899 0.0619 1.1925 0.1094 0.0615 1.1929 −0.5898 0.0547 1.1932−0.5704 0.0554 1.1934 −0.5511 0.0562 1.1936 −0.5318 0.0569 1.1939−0.5125 0.0575 1.1941 −0.4933 0.0581 1.1943 −0.4740 0.0587 1.1946−0.4548 0.0593 1.1948 −0.4355 0.0598 1.1950 −0.4162 0.0602 1.1952−0.3969 0.0606 1.1954 −0.3775 0.0609 1.1956 −0.3580 0.0611 1.1957−0.3386 0.0613 1.1959 −0.3191 0.0615 1.1960 −0.2996 0.0616 1.1962−0.2800 0.0616 1.1964 −0.2605 0.0616 1.1965 −0.2409 0.0616 1.1967−0.2212 0.0616 1.1969 −0.2016 0.0616 1.1971 −0.1819 0.0616 1.1973−0.1622 0.0616 1.1975 −0.1425 0.0616 1.1977 −0.1228 0.0616 1.1980−0.1031 0.0617 1.1983 −0.0835 0.0617 1.1986 −0.0639 0.0617 1.1989−0.0443 0.0618 1.1992 −0.0248 0.0618 1.1992 −0.8604 0.0419 1.1994−0.8409 0.0430 1.1995 −0.0052 0.0617 1.1995 −0.8213 0.0440 1.1998 0.01440.0616 1.2001 0.0340 0.0615 1.2003 0.0536 0.0612 1.2006 0.0732 0.06091.2008 0.0927 0.0606 1.2013 −0.6261 0.0526 1.2015 −0.6066 0.0534 1.2017−0.5872 0.0542 1.2020 −0.5678 0.0549 1.2022 −0.5485 0.0556 1.2024−0.5292 0.0562 1.2026 −0.5100 0.0569 1.2029 −0.4907 0.0575 1.2031−0.4715 0.0580 1.2033 −0.4522 0.0585 1.2035 −0.4329 0.0590 1.2037−0.4135 0.0594 1.2039 −0.3942 0.0597 1.2041 −0.3748 0.0600 1.2043−0.3553 0.0603 1.2045 −0.3359 0.0605 1.2046 −0.3164 0.0607 1.2048−0.2969 0.0608 1.2050 −0.2774 0.0609 1.2052 −0.2578 0.0610 1.2053−0.2382 0.0610 1.2055 −0.2186 0.0611 1.2057 −0.1989 0.0611 1.2059−0.1792 0.0611 1.2062 −0.1595 0.0612 1.2064 −0.1398 0.0612 1.2066−0.1201 0.0612 1.2069 −0.1004 0.0612 1.2072 −0.0808 0.0612 1.2074−0.0611 0.0611 1.2077 −0.0415 0.0611 1.2079 −0.8569 0.0409 1.2080−0.0219 0.0610 1.2080 −0.8374 0.0420 1.2082 −0.0023 0.0608 1.2082−0.8179 0.0431 1.2085 0.0174 0.0606 1.2087 0.0371 0.0603 1.2090 0.05670.0600 1.2092 0.0762 0.0596 1.2094 0.0955 0.0592 1.2099 −0.6425 0.05131.2102 −0.6231 0.0521 1.2104 −0.6036 0.0528 1.2106 −0.5843 0.0536 1.2108−0.5650 0.0543 1.2110 −0.5457 0.0549 1.2112 −0.5264 0.0556 1.2114−0.5071 0.0562 1.2117 −0.4879 0.0567 1.2119 −0.4686 0.0573 1.2121−0.4493 0.0577 1.2123 −0.4299 0.0582 1.2125 −0.4106 0.0586 1.2127−0.3912 0.0589 1.2129 −0.3718 0.0592 1.2131 −0.3524 0.0595 1.2132−0.3330 0.0598 1.2134 −0.3135 0.0600 1.2136 −0.2940 0.0601 1.2138−0.2745 0.0603 1.2140 −0.2549 0.0604 1.2142 −0.2353 0.0605 1.2144−0.2156 0.0605 1.2146 −0.1959 0.0606 1.2148 −0.1762 0.0606 1.2151−0.1564 0.0606 1.2153 −0.1367 0.0606 1.2155 −0.1170 0.0606 1.2158−0.0973 0.0606 1.2160 −0.0776 0.0605 1.2162 −0.0580 0.0604 1.2164−0.8727 0.0390 1.2165 −0.0383 0.0602 1.2166 −0.8533 0.0401 1.2167−0.0186 0.0600 1.2168 −0.8339 0.0413 1.2170 0.0011 0.0598 1.2170 −0.81450.0423 1.2172 0.0208 0.0595 1.2174 0.0404 0.0592 1.2176 0.0599 0.05881.2178 0.0792 0.0584 1.2180 0.0987 0.0579 1.2186 −0.6587 0.0499 1.2188−0.6392 0.0507 1.2190 −0.6198 0.0515 1.2192 −0.6005 0.0522 1.2194−0.5811 0.0530 1.2196 −0.5618 0.0536 1.2198 −0.5426 0.0543 1.2200−0.5233 0.0549 1.2203 −0.5040 0.0555 1.2205 −0.4847 0.0560 1.2207−0.4654 0.0565 1.2209 −0.4461 0.0570 1.2211 −0.4267 0.0574 1.2213−0.4074 0.0578 1.2215 −0.3880 0.0582 1.2217 −0.3686 0.0585 1.2219−0.3492 0.0588 1.2221 −0.3298 0.0591 1.2223 −0.3103 0.0593 1.2225−0.2908 0.0595 1.2227 −0.2713 0.0596 1.2229 −0.2517 0.0598 1.2231−0.2320 0.0599 1.2233 −0.2123 0.0600 1.2235 −0.1926 0.0600 1.2237−0.1728 0.0600 1.2240 −0.1531 0.0600 1.2242 −0.1333 0.0600 1.2244−0.1136 0.0599 1.2246 −0.0939 0.0598 1.2248 −0.0742 0.0597 1.2251−0.0545 0.0595 1.2252 −0.8690 0.0383 1.2253 −0.0348 0.0593 1.2254−0.8496 0.0395 1.2255 −0.0151 0.0591 1.2256 −0.8302 0.0406 1.2257 0.00460.0588 1.2258 −0.8109 0.0417 1.2259 0.0243 0.0585 1.2261 0.0438 0.05811.2263 0.0631 0.0577 1.2265 0.0825 0.0573 1.2270 −0.6941 0.0476 1.2272−0.6746 0.0485 1.2274 −0.6552 0.0493 1.2276 −0.6357 0.0501 1.2279−0.6164 0.0509 1.2281 −0.5970 0.0516 1.2283 −0.5777 0.0523 1.2285−0.5585 0.0530 1.2287 −0.5392 0.0536 1.2289 −0.5199 0.0542 1.2291−0.5006 0.0548 1.2293 −0.4813 0.0553 1.2295 −0.4620 0.0558 1.2297−0.4427 0.0563 1.2299 −0.4233 0.0567 1.2301 −0.4040 0.0571 1.2303−0.3846 0.0575 1.2305 −0.3652 0.0578 1.2307 −0.3458 0.0581 1.2309−0.3263 0.0584 1.2311 −0.3068 0.0586 1.2313 −0.2873 0.0588 1.2316−0.2677 0.0590 1.2318 −0.2481 0.0591 1.2320 −0.2284 0.0592 1.2322−0.2086 0.0593 1.2324 −0.1889 0.0593 1.2326 −0.1691 0.0593 1.2328−0.1494 0.0593 1.2330 −0.1296 0.0592 1.2332 −0.1099 0.0591 1.2334−0.0902 0.0590 1.2337 −0.0705 0.0588 1.2339 −0.0508 0.0586 1.2340−0.8652 0.0378 1.2341 −0.0310 0.0584 1.2342 −0.8458 0.0389 1.2343−0.0113 0.0581 1.2344 −0.8264 0.0400 1.2345 0.0083 0.0578 1.2346 −0.80710.0411 1.2347 0.0278 0.0575 1.2348 −0.7877 0.0422 1.2349 0.0471 0.05711.2351 0.0666 0.0567 1.2353 0.0862 0.0563 1.2355 −0.7293 0.0452 1.2357−0.7098 0.0461 1.2359 −0.6903 0.0470 1.2361 −0.6708 0.0479 1.2363−0.6514 0.0487 1.2365 −0.6320 0.0495 1.2367 −0.6127 0.0503 1.2369−0.5934 0.0510 1.2371 −0.5742 0.0517 1.2373 −0.5549 0.0523 1.2375−0.5356 0.0530 1.2377 −0.5163 0.0535 1.2379 −0.4970 0.0541 1.2381−0.4777 0.0546 1.2383 −0.4584 0.0551 1.2385 −0.4390 0.0556 1.2388−0.4197 0.0560 1.2390 −0.4003 0.0564 1.2392 −0.3809 0.0568 1.2394−0.3615 0.0571 1.2396 −0.3421 0.0574 1.2398 −0.3226 0.0577 1.2400−0.3031 0.0579 1.2402 −0.2835 0.0581 1.2404 −0.2638 0.0583 1.2406−0.2441 0.0584 1.2408 −0.2244 0.0585 1.2410 −0.2046 0.0585 1.2412−0.1849 0.0586 1.2415 −0.1651 0.0586 1.2417 −0.1454 0.0585 1.2419−0.1257 0.0584 1.2421 −0.1060 0.0583 1.2423 −0.0863 0.0582 1.2425−0.0665 0.0580 1.2427 −0.0468 0.0578 1.2429 −0.8611 0.0372 1.2429−0.0271 0.0576 1.2431 −0.8418 0.0384 1.2431 −0.0074 0.0573 1.2433−0.8224 0.0395 1.2433 0.0121 0.0570 1.2435 −0.8030 0.0406 1.2435 0.03130.0566 1.2437 −0.7836 0.0417 1.2438 0.0508 0.0563 1.2439 −0.7642 0.04271.2440 0.0704 0.0558 1.2441 −0.7447 0.0437 1.2442 0.0899 0.0554 1.2443−0.7252 0.0446 1.2445 −0.7057 0.0456 1.2447 −0.6862 0.0464 1.2449−0.6668 0.0473 1.2451 −0.6475 0.0481 1.2453 −0.6281 0.0489 1.2456−0.6089 0.0497 1.2458 −0.5896 0.0504 1.2460 −0.5703 0.0510 1.2462−0.5511 0.0517 1.2464 −0.5318 0.0523 1.2466 −0.5125 0.0529 1.2468−0.4932 0.0535 1.2470 −0.4739 0.0540 1.2472 −0.4545 0.0545 1.2474−0.4352 0.0549 1.2476 −0.4158 0.0553 1.2478 −0.3964 0.0557 1.2480−0.3770 0.0561 1.2482 −0.3576 0.0564 1.2484 −0.3381 0.0567 1.2486−0.3186 0.0569 1.2488 −0.2990 0.0572 1.2491 −0.2794 0.0574 1.2493−0.2597 0.0575 1.2495 −0.2399 0.0576 1.2497 −0.2202 0.0577 1.2499−0.2004 0.0578 1.2501 −0.1807 0.0578 1.2503 −0.1610 0.0578 1.2505−0.1412 0.0577 1.2507 −0.1215 0.0577 1.2509 −0.1018 0.0576 1.2511−0.0821 0.0574 1.2514 −0.0624 0.0572 1.2515 −0.8763 0.0356 1.2516−0.0427 0.0570 1.2517 −0.8569 0.0367 1.2518 −0.0230 0.0567 1.2519−0.8376 0.0379 1.2520 −0.0035 0.0565 1.2521 −0.8182 0.0390 1.2522 0.01580.0561 1.2523 −0.7988 0.0401 1.2524 0.0352 0.0558 1.2525 −0.7793 0.04111.2526 0.0548 0.0554 1.2527 −0.7598 0.0421 1.2528 0.0744 0.0550 1.2530−0.7403 0.0431 1.2532 −0.7208 0.0441 1.2534 −0.7014 0.0450 1.2536−0.6820 0.0459 1.2538 −0.6627 0.0467 1.2540 −0.6433 0.0475 1.2542−0.6241 0.0483 1.2544 −0.6048 0.0490 1.2546 −0.5856 0.0497 1.2548−0.5663 0.0504 1.2550 −0.5470 0.0511 1.2552 −0.5277 0.0517 1.2554−0.5084 0.0523 1.2556 −0.4891 0.0528 1.2558 −0.4698 0.0533 1.2560−0.4504 0.0538 1.2562 −0.4311 0.0542 1.2564 −0.4117 0.0547 1.2567−0.3923 0.0550 1.2569 −0.3729 0.0554 1.2571 −0.3534 0.0557 1.2573−0.3339 0.0560 1.2575 −0.3143 0.0562 1.2577 −0.2947 0.0565 1.2579−0.2750 0.0566 1.2581 −0.2552 0.0568 1.2583 −0.2355 0.0569 1.2585−0.2157 0.0570 1.2587 −0.1960 0.0570 1.2589 −0.1763 0.0570 1.2592−0.1566 0.0570 1.2594 −0.1369 0.0570 1.2596 −0.1171 0.0569 1.2598−0.0974 0.0568 1.2600 −0.0777 0.0566 1.2602 −0.0580 0.0564 1.2603−0.8718 0.0351 1.2604 −0.0383 0.0562 1.2605 −0.8525 0.0362 1.2606−0.0189 0.0559 1.2608 −0.8331 0.0374 1.2608 0.0004 0.0556 1.2610 −0.81370.0385 1.2610 0.0198 0.0553 1.2612 −0.7942 0.0396 1.2612 0.0394 0.05501.2614 −0.7747 0.0406 1.2614 0.0590 0.0546 1.2616 −0.7552 0.0416 1.26170.0785 0.0541 1.2618 −0.7358 0.0426 1.2620 −0.7163 0.0435 1.2622 −0.69690.0444 1.2624 −0.6776 0.0453 1.2626 −0.6583 0.0461 1.2628 −0.6390 0.04691.2630 −0.6198 0.0477 1.2632 −0.6005 0.0484 1.2634 −0.5813 0.0491 1.2636−0.5620 0.0498 1.2638 −0.5427 0.0504 1.2640 −0.5234 0.0510 1.2643−0.5041 0.0516 1.2645 −0.4848 0.0522 1.2647 −0.4654 0.0527 1.2649−0.4461 0.0531 1.2651 −0.4267 0.0536 1.2653 −0.4073 0.0540 1.2655−0.3879 0.0544 1.2657 −0.3684 0.0547 1.2659 −0.3489 0.0550 1.2661−0.3293 0.0553 1.2663 −0.3097 0.0555 1.2665 −0.2900 0.0557 1.2667−0.2703 0.0559 1.2669 −0.2505 0.0561 1.2672 −0.2308 0.0562 1.2674−0.2111 0.0562 1.2676 −0.1914 0.0563 1.2678 −0.1716 0.0563 1.2680−0.1519 0.0563 1.2682 −0.1322 0.0562 1.2684 −0.1125 0.0561 1.2686−0.0928 0.0560 1.2688 −0.0731 0.0558 1.2690 −0.8864 0.0334 1.2690−0.0535 0.0556 1.2692 −0.8671 0.0346 1.2692 −0.0340 0.0554 1.2694−0.8477 0.0358 1.2695 −0.0147 0.0551 1.2696 −0.8283 0.0369 1.2697 0.00470.0548 1.2698 −0.8089 0.0380 1.2699 0.0243 0.0545 1.2700 −0.7894 0.03911.2701 0.0439 0.0541 1.2702 −0.7699 0.0401 1.2703 0.0634 0.0537 1.2704−0.7504 0.0411 1.2705 0.0829 0.0533 1.2706 −0.7310 0.0421 1.2708 −0.71160.0430 1.2710 −0.6923 0.0439 1.2712 −0.6730 0.0447 1.2714 −0.6537 0.04561.2716 −0.6345 0.0464 1.2718 −0.6153 0.0471 1.2720 −0.5960 0.0478 1.2722−0.5768 0.0485 1.2724 −0.5575 0.0492 1.2727 −0.5382 0.0498 1.2729−0.5189 0.0504 1.2731 −0.4995 0.0510 1.2733 −0.4802 0.0515 1.2735−0.4609 0.0520 1.2737 −0.4415 0.0525 1.2739 −0.4221 0.0529 1.2741−0.4027 0.0533 1.2743 −0.3832 0.0537 1.2745 −0.3637 0.0540 1.2747−0.3441 0.0543 1.2749 −0.3245 0.0546 1.2751 −0.3048 0.0548 1.2753−0.2851 0.0550 1.2756 −0.2654 0.0552 1.2758 −0.2456 0.0553 1.2760−0.2259 0.0554 1.2762 −0.2062 0.0555 1.2764 −0.1865 0.0555 1.2766−0.1668 0.0555 1.2768 −0.1471 0.0555 1.2770 −0.1274 0.0554 1.2772−0.1076 0.0553 1.2774 −0.0880 0.0552 1.2776 −0.0683 0.0550 1.2777−0.8815 0.0329 1.2779 −0.0488 0.0548 1.2779 −0.8621 0.0341 1.2781−0.0295 0.0545 1.2781 −0.8427 0.0353 1.2783 −0.0101 0.0543 1.2784−0.8233 0.0364 1.2785 0.0095 0.0540 1.2786 −0.8038 0.0375 1.2787 0.02910.0536 1.2788 −0.7843 0.0386 1.2789 0.0486 0.0532 1.2790 −0.7649 0.03961.2791 0.0680 0.0528 1.2792 −0.7454 0.0406 1.2794 −0.7261 0.0415 1.2796−0.7067 0.0425 1.2798 −0.6874 0.0433 1.2800 −0.6682 0.0442 — — — — — —

While the invention is described with reference to exemplaryembodiments, it will be understood by those skilled in the art thatvarious changes may be made and equivalents may be substituted withoutdeparting from the spirit and scope of the invention, and modificationsmay be made to adapt particular situations or materials to the teachingsof the invention without departing from the essential scope thereof. Theinvention is thus not limited to the particular embodiments disclosedherein, but includes all embodiments falling within the scope of theappended claims.

1. An airfoil comprising: an external surface formed in substantialconformance with a plurality of cross sections of the airfoil, each ofthe cross sections having an axial chord and an offset at acorresponding fractional span as set forth in Table 2 herein; whereineach of the cross sections is described by a set of Cartesiancoordinates defined at the corresponding fractional span as set forth inTable 4 herein.
 2. The airfoil of claim 1, wherein each of the crosssections comprises a chord length defined by scaling the axial chord toa root chord of the airfoil, a height defined by scaling the fractionalspan to a span height of the airfoil, and a displacement defined byscaling the offset to the root chord and a root pitch of the airfoil. 3.The airfoil of claim 2, wherein each of the cross sections comprises aset of airfoil coordinates describing the external surface, the airfoilcoordinates being determined by scaling the set of Cartesian coordinatesto the chord length and adding the displacement.
 4. The airfoil of claim2, wherein each of the cross sections comprises a radial heightdetermined by adding a root radius of the airfoil to the height of thecross section, and wherein the root radius is between 4.0 inches and 8.0inches (or between 102 mm and 203 mm).
 5. The airfoil of claim 2,wherein the span height is between 1.0 inches and 2.0 inches (or between25.4 mm and 50.8 mm).
 6. The airfoil of claim 5, wherein the span heightis about 1.56±0.05 inches (or about 39.6±1.3 mm) and the root radius isabout 6.70±0.10 inches (or about 170.2±2.5 mm).
 7. The airfoil of claim3, wherein the span height is between 0.5 inches and 2.5 inches (orbetween 12.7 mm and 63.5 mm), wherein the root chord is between 0.375inches and 1.5 inches (or between 9.5 mm and 38.1 mm), and wherein theroot pitch is between 0.5 inches and 2.0 inches (or between 12.7 mm and50.8 mm).
 8. The airfoil of claim 7, wherein the span height is about1.56±0.05 inches (or about 39.6±1.3 mm), wherein the root chord is about0.74±0.05 inches (or about 18.8±1.3 mm), and wherein the root pitch isabout 0.96±0.05 inches (or about 24.4±1.3 mm).
 9. The airfoil of claim1, further comprising a platform attached to the airfoil at a rootsection.
 10. The airfoil of claim 9, wherein the platform is defined inconformance with platform coordinates as set forth in Table 6 herein.11. A blade comprising: an airfoil formed in substantial conformancewith a plurality of cross sections defining an external surface of theblade; and a platform attached to a root section of the airfoil; whereineach of the cross sections has an axial chord and an offset at acorresponding fractional span as set forth in Table 2 herein; andwherein each of the cross sections is described by a set of Cartesiancoordinates defined at the corresponding fractional span as set forth inTable 4 herein.
 12. The blade of claim 11, wherein the platform isformed in substantial conformance with platform coordinates as set forthin Table 6 herein.
 13. The blade of claim 11, wherein each of the crosssections comprises a set of airfoil coordinates defined on the externalsurface of the blade by scaling the set of Cartesian coordinates to thechord length and adding the displacement.
 14. The blade of claim 13,wherein each of the cross sections comprises a height defined by scalingthe fractional span to a span height between 1.0 inches and 2.0 inches(or between 25.4 mm and 50.8 mm).
 15. The blade of claim 14, whereineach of the cross sections comprises: a chord length defined by scalingthe axial chord to a root chord between 0.5 inches and 1.0 inches (orbetween 12.7 mm and 25.4 mm); and a displacement defined by scaling theoffset to the root chord and a root pitch between 0.5 inches and 1.5inches (or between 12.7 mm and 38.1 mm).
 16. A turbine assemblycomprising: a plurality of rotor airfoils arranged circumferentiallyabout a turbine axis, each of the rotor airfoils being formed insubstantial conformance with a plurality of blade sections, each of theblade sections having an axial chord and an offset at a correspondingfractional span as set forth in Table 2 herein; wherein each of theblade sections is described by a set of Cartesian coordinates defined atthe corresponding fractional span as set forth in Table 4 herein. 17.The turbine assembly of claim 16, further comprising a plurality ofstator airfoils arranged circumferentially about the turbine axis, eachof the stator airfoils being formed in substantial conformance with aplurality of vane sections, each of the vane sections having an axialchord and an offset at a corresponding fractional span as set forth inTable 1 herein, wherein each of the vane sections is described by a setof Cartesian coordinates defined at the corresponding fractional span asset forth in Table 3 herein.
 18. The turbine assembly of claim 17,wherein each of the rotor airfoils and each of the stator airfoils has aspan height between 1.0 inches and 2.0 inches (or between 25.4 mm and50.8 mm).
 19. The turbine assembly of claim 18, further comprising aplurality of platforms coupled to the plurality of blade airfoils toform an inner diameter flowpath about the turbine axis in substantialconformance with platform coordinates as set forth in Table 6 herein.20. The turbine assembly of claim 19, wherein the plurality of bladeairfoils consists of forty-four blade airfoils and the plurality ofstator airfoils consists of forty-four vane airfoils.